find a nonzero matrix a such that a2=0

One easy one is the matrix with a single $1$ on the diagonal above the principal. What maths knowledge is required for a lab-based (molecular and cell biology) PhD? What does "Welcome to SeaWorld, kid!" Find a non-zero matrix that fulfills the requirements in the photo, Step by stepSolved in 2 steps with 1 images, A: Given matrix isA=221442110. Solution: Since A is diagonalizable, there exists an invertible matrix P and a diagonal matrix D such that A = PDP 1: Since A is invertible, then = 0 is not an eigenvalue of A; so that all of the diagonal entries of D are nonzero, and so D is also invertible. Note that this is equivalent to the solution by Focus, given the comment I made there. Let $A$ be a matrix. Can I trust my bikes frame after I was hit by a car if there's no visible cracking. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Let A be an nn matrix in which the entries of each row sum to zero. The resulting matrix is, $$ %3D, James Stewart, Lothar Redlin, Saleem Watson, Find a non-zero 2 2 matrix A such that A2 = A =, Elementary Linear Algebra (MindTap Course List), Algebra and Trigonometry (MindTap Course List). I don't understand: you want a matrix $A\neq 0$ such that for all $B\neq 0$, $AB=0$. \end{pmatrix}. Try it in the Numerade app? Find a non-zero 2 x 2 matrix A such that A2 0 0 A= E = Hint: A cannot have ALL entries be zeros according to the instructions, but you CAN let one whole row or one whole column be all zeros to make calculations easier. the matrix must be square. A vector in the null space is any vector, v, such that Av= 0. What is this object inside my bathtub drain that is causing a blockage? Here again, Id try to keep it simple, so Id look for linear transformations sending $R^2$ to itself. A can be the matrix such that, multiplying any vector (x, y, z) by A, changes the vector by "pushing" every number in the vector down one position, and putting 0 at the top. Thank you very much again. The best answers are voted up and rise to the top, Not the answer you're looking for? How do you find a non zero vector in Linear Algebra? Doesn't the solution show that $A := \mathbf{cr^T}$ does beget a counterexample, such as the one in my OP? Definition Let A be an n n matrix. 1 (a) Find a nonzero matrix A for which A 2 = 0. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. I'm asked to to find a $3\times3$ matrix, in which no entry is $0$ but $A^2=0$. $\alpha = \begin{pmatrix} 1 \\ 1\\ 1 \end{pmatrix}, \beta = \begin{pmatrix} what is the best way to find the maximum non-zero matrix(ie. Noise cancels but variance sums - contradiction? Is it possible for rockets to exist in a world that is only in the early stages of developing jet aircraft? B can be any non-zero matrix. The subspace of a vector space is a non-empty subset of the vector space over the same, A: Given : The given series is :n=1un=n=14n29n4+1. Two attempts of an if with an "and" are failing: if [ ] -a [ ] , if [[ && ]] Why? Taking the cross product of $a_1$ and $a_2$ is the easiest way to find such a vector, but another way would be to calculate the. You describe your situation with a transition matrix. Determine whether the matrix is in row-echelon form. Thanks! 0 & 0& 0 \\ Robert J. Connect and share knowledge within a single location that is structured and easy to search. Learn more about Stack Overflow the company, and our products. So $$(a,-a,0) \cdot (1,1,0)=0$$ and $$(a,-a,0) \cdot (1,1,1)=0$$ for any $a \in \mathbb{R}$. Matrices is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. Step by stepSolved in 4 steps with 3 images, A: The given problem is to find the Fourier series expansion of the given periodic function with period. In general, it is difficult to show that two matrices are similar. (b) Find a matrix that has A 2 0 but A 3 = 0. Find two nonzero matrices A and B such that AB=BA. So we can modify the matrix above, which we'll call $D$, to get a matrix with no zeros. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. First week only $4.99! In mathematical language, the question asks whether it is possible for a 10 12 matrix A to have dimNulA = 1. 576), AI/ML Tool examples part 3 - Title-Drafting Assistant, We are graduating the updated button styling for vote arrows. What is the procedure to develop a new force field for molecular simulation? Note that with $\alpha^T=(1, d/a, e/a); \beta^T=(a, b, c)$ this gives Henry's solution. It is one of many possible choices: anything in the span of the column space will do. Axial compressive load (p) = 320 To find the entries of this A, multiply A by each vector in the standard basis, and these results are the columns of A. In July 2022, did China have more nuclear weapons than Domino's Pizza locations? where b and c can be any non-zero number. What happens if you've already found the item an old map leads to? Is there a reliable way to check if a trigger being fired was the result of a DML action from another *specific* trigger? What is the procedure to develop a new force field for molecular simulation? \quad \blacksquare$, (b) Since I chose $\mathbf{c, r}$ such that $\mathbf{\color{green}{r^Tc = 0}}$, thus $A^3 = \mathbf{c\color{green}{r^Tc}\color{green}{r^Tc}r^T} = 0.$. Construct a 2x2 matrix B such that AB is the zero matrix. 0 & 0 & 0 & 0 \\ answered 11/17/13, Certified High School AP Calculus and Physics Teacher, Andre W. For the null space, notice that first and third columns of $A$ are equal, which means that, $$A\begin{bmatrix} 1 \\ 0 \\ -1 \\ 0\end{bmatrix} = 0.$$. 0 & 0 & 0 & 0 \\ $$ 4 & 3 & -2 & -9 \\ 1 B 0 C -1 D none of these Medium Solution Verified by Toppr Correct option is B) If A=0,tr(A)=0. perpendicular to the two vectors. Upvoted. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. 22. In general, it is difficult to show that two matrices are similar. A: INTRODUCTION: If so, find an example. 6& 12& 18\\ Why does it work. A: We have to find the diagonal matrix if possible. This problem has been solved! Thus, for want of a counterexample, choose $\mathbf{r} = (0,k)$ and $\mathbf{c} = (k,0)^T. For simplicity, assume a 22 matrix. Now let's jump onto the solution of the question. Ohh your edit helped. If $A^{n-1} \neq \bf{0}$ but $A^{n} = \bf{0}$, what does it say about the matrix $A$? If not, prove why not. 0 & 0 & 0 Did an AI-enabled drone attack the human operator in a simulation environment? Best answer Example 1 : Let A = [ 1 0 0 0] [ 1 0 0 0] and B = [ 0 0 0 1] [ 0 0 0 1] are the two non - zero matrices. To do this, first consider a trivial matrix with lots of zeros that does satisfy this condition. Should I include non-technical degree and non-engineering experience in my software engineer CV? In the analysis of linear, A: Solving Part C only ..as you have already mentioned :-, A: Thanks for the question :)And your upvote will be really appreciable ;), A: The objective is to find the matrix B. heck whether the matrix B is diagonalizable or not and also. Get the app to make the most of your account. Can a matrix with zeros on the diagonal have an inverse? 2x+y-z=3,, A: Introduction: Thank you very much. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. The vectors that form a basis for the column space are certainly in the column space. I started with the zero-matrix and then checked where I can put something non-zero so that A is still the zero-matrix. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. The best answers are voted up and rise to the top, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. How to find the maximum value in a zeros array in python? -5 & -5 & 1 & 14 \\ the undeniable fact that the Matrix A is nonzero does no longer mean that the Determinant is nonzero. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. Such that My a squared is equal to zero. h:a,b is bounded and Riemann integrable andhx0 for allxa,b, To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Theoretical Approaches to crack large files encrypted with AES, Citing my unpublished master's thesis in the article that builds on top of it. By the way the maximum non-zero matrix, in this case, is the original matrix itself. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. = [ ]. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The vectors $a_1 = (1, 1, 0)$ and $a_2 = (1, 1, 1)$ span a plane in $\Bbb R^3$. (b) Assume B is a nonzero n x n matrix such that B-0. Then find an invertible matrix P such . On the first morning you can only wake up in the first or second room. f'(x)=ddx(tan(x)-13csc(x)+4)=sec2(x)+. $$ M^3 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} $$. \begin{bmatrix} $$. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Find a 2x2 matrix B that is not the zero matrix such that AB is the zero matrix. The question is; and all thats needed in order to finish the job is to find $a,b,c$, and $d$ so that $ac+bd=0$, at least one of $a$ and $b$ is non-zero, and at least one of $c$ and $d$ is non-zero; this is very easy to do. rev2023.6.2.43474. Connect and share knowledge within a single location that is structured and easy to search. One can also contemplate over why you can never find a $2 \times 2$ matrix that works for case 2. We have $n\cdot v=0$. Construct a 2x2 matrix B such that AB . To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Thanks for contributing an answer to Stack Overflow! But entries of $B^{-1}$ are just the cofactors of $B$, with some sign, divided by the determinant. Then, $A^2 = \alpha \beta' \alpha \beta'$, so if $\alpha,\beta \ne 0$(all the components are not $0$),$\beta' \alpha = 0$ things will be solved. rev2023.6.2.43474. To get a vector in the column space, take any one of the . But if you take $B=I$? If $A^2 =0$, then $C^2 = B^{-1}ABB^{-1}AB = B^{-1}A^2B =0$. I then attempted to express A as such that A 2 = =-I, but it this didn't lead me anywhere either. Find centralized, trusted content and collaborate around the technologies you use most. Coach tickets as y, where y>40. Movie in which a group of friends are driven to an abandoned warehouse full of vampires. By trial and error find real nonzero 2 by 2 matrices such that {A}^ {2}=-I \quad BC=0 \quad DE=-ED A2 = I BC = 0 DE = E D (not allowing DE=0). Noise cancels but variance sums - contradiction? For the null space, notice that first and third columns of A A are equal, which means that. "I don't like it when it is rainy." p=5x2+2x+3 If I make the bottom row of A all zeroes, the bottom row of A B will automatically be all zeroes. (PLEASE NOTE : I expect this to be a simple task for you. [Strang P131 3.1.31], Free variables, nullspace for a matrix with the sum of certain columns = zero vector [Strang P142 3.2.20]. Why are mountain bike tires rated for so much lower pressure than road bikes? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. My result regarding to question 1 is given below(Calculated in maple): Then, my question is how to solve the question 2? Final answer Step 1/2 We have to find non-zero 2 x 2 matrix such that , View the full answer Step 2/2 Final answer Transcribed image text: Find a non-zero 2 x 2 matrix such that 0 01 27 -24 Previous question Next question This problem has been solved! No packages or subscriptions, pay only for the time you need. Support a apart one rather. The Kb of pyridine, C5H5N, is 1.5 x 10-9. A: Given:A=-6669-8-12-334 My initial attempt at the problem involved multiplying both sides of the equation by the inverse of A in attempt to isolate A, that only produced IA=-A -1 which is really no more clear than what I started with. Find |A|. It is of fundamental importance in many areas and is the subject of our study for this chapter. A: We have to find the formula for given integral. arrow_forward. (3) det(cA). so we will not end that A is invertible. 11. Can Bluetooth mix input from guitar and send it to headphones? Must it be true that A=D? To get a vector in the row space take any one of the rows of the matrix. Experts are tested by Chegg as specialists in their subject area. My father is ill and booked a flight to see him - can I travel on my other passport? iPad. Free Variables in a Reduced Matrix - How do they affect rows filled with zeros? Click 'Join' if it's correct. Number of solutions in system of linear equations. when you have Vim mapped to always print two? The matrices have the property : \displaystyle A^k = 0 Ak = 0 where A is a square matrix and k is a positive integer. In Europe, do trains/buses get transported by ferries with the passengers inside? Matrix. A: Given, - user148177 0 & 0 & 0 & 0 \\ Use two different nonzero columns for B. I know I can put some variables in B and then multiply AB and then that equation = 0, but I still can't seem to crack it. (15Find the complete set of solutions to the following system of equations: 2x2 3x1 + 8x2 2x1 + 7x2 x1 + 3x2 x3 + 4x3 + 3x3 + 2x3 2x4 = 12x4 = 14x4 = 2= 0 Solution. I was confused for a while. Prove that (In -3B) is invertible and (In-3B)"! Learn more about Stack Overflow the company, and our products. Don't have to recite korbanot at mincha? Assume that you work in a algebra closed field. Discuss. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. I'd like: A 2 = c r T c r T = 0. r T c = 0 would imply this. What is the procedure to develop a new force field for molecular simulation? This gets the minimum index of np.nonzero as the start range, and the maximum index of np.nonzero as the end range, in both axis. Can the logo of TSR help identifying the production time of old Products? Diameter (d)= 200 mm VS "I don't like it raining.". Find two 2 x 2 matrices A such that A 2 = O. Unlock this answer and thousands more Step-by-Step Solved solutions by becoming a member. A: Here the given matrix isA=1140-40-5-1-8 On arrival you could be in any room. Should I include non-technical degree and non-engineering experience in my software engineer CV? Whatever you do amounts to choosing a basis for a vector space. Take a simple example and rotate the co-ordinate axes. What is the minimum rank of a 53 matrix? So we get, \begin{pmatrix}0&0&0\\1&0&0\\0&1&0\end{pmatrix}. What is the procedure to develop a new force field for molecular simulation? Here's an interesting review question I have: Find a nonzero matrix, so that when it is multiplied by another nonzero matrix, the zero matrix is the result. If you project your space onto a line $\ell$ and then rotate this line by $90^\circ$ degree, all vectors are now orthogonal to the line $\ell$. 35,000 worksheets, games, and lesson plans, Marketplace for millions of educator-created resources, Spanish-English dictionary, translator, and learning, Diccionario ingls-espaol, traductor y sitio de aprendizaje, If the product is a zero matrix, you must have. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Almost done! Educator app for $$ M^2 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ \frac 16 & 0 & 0 \end{bmatrix} $$ Use the. Find two nonzero matrices and such that. What maths knowledge is required for a lab-based (molecular and cell biology) PhD? In linear algebra, eigenvalues are related to eigenvectors. You can choose one of these. Start your trial now! [GStrang P194 3.6.42], Provided $A$'s distinct eigenvalues, show that $Ax = u$ has no solution. I want AB = 0 when A 0 and B 0. Not the answer you're looking for? $\Large{2. For the row space, pick any (nonzero) row. Does the policy change for AI-generated content affect users who (want to) Matrix operation in python, maximum value, find row or column containing maximum value in numpy array, Python List. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. For part (a), just take a square matrix $A$ larger than 1-by-1 filled almost entirely with zeros and $A^2$ is probably $0$. Their cross product is perpendicular to the vectors! Download link will automatically paste in the promo code on the sign up screen, Best Matched Videos Solved By Our Top Educators, First, we need to find a 2x2 matrix A such that when we multiply A by itself (A^2), we get the zero matrix. However, is this the best way? If you are using inverses, what do you want to take the inverse of? This is not a $3 \times 3$ matrix though. See Answer Question: Find a non-zero 2 x 2 matrix A such that A2 = [0 ] A = Show transcribed image text Expert Answer Transcribed image text: Find a non-zero 2 x 2 matrix A such that A2 = [0 ] A = To get a vector in the column space, take any one of the columns of the matrix. f(x)=tan(x)-13csc(x)+4 The problem is if I I brute force it, I am left with a system of 6 equations (Not all of which are linear) and 6 unknowns. Is every linear transform that takes a non-zero vector to zero composed of a projection? You will get that each entry of the matrix $B^{-1}DB$ actually looks like some entry(in fact, an entry of the first column) of $B^{-1}$ times some entry of $B$. By clicking Post Your Answer, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct. Two attempts of an if with an "and" are failing: if [ ] -a [ ] , if [[ && ]] Why? A: Given A for loop iteration can be performed over the rows and columns to access the cell values contained in a matrix. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Find a nonzero matrix, so that when it is multiplied by another nonzero matrix, the zero matrix is the result. @LePressentiment : Did you use some software to translate this question into English? We have to find nine zero 3-plus 3. $\Large{1. point) Find a non-zero 2 X 2 matrix such that-6 -8 24%]: Geometrically find a 2x2 matrix A such that A^2 = -I_2, point) Find a non-zero 2 X2 matrix such that-1-6 24[o %, Find a $2 \times 2$ matrix $A$ such that $A^{2}$ is diagonal but not $A.$. On each. I ve gone through numpy.nonzero which gives the indices of non zero elements but how can i use it efficiently to get the expected matrix? Expert Answer On the third morning there is nowhere you can be. I'm in doubt what even to do. [GStrang P130 3.1.27], Without elimination, find bases for the four subspaces for this matrix. How appropriate is it to post a tweet saying that I am looking for postdoc positions? Most likely yes. To attain moksha, must you be born as a Hindu? How much of the power drawn by a chip turns into heat? You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 11. Just intuition? Free family = linearly independent (ordered) set of vectors. How appropriate is it to post a tweet saying that I am looking for postdoc positions? Does substituting electrons with muons change the atomic shell configuration? Reduce the matrix to identity matrix form by performing, A: Let A be an nk matrix, for some positive integers n and k. Movie in which a group of friends are driven to an abandoned warehouse full of vampires, Theoretical Approaches to crack large files encrypted with AES. Also it wont work if the matrix does not start at 0. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. It leads to X = . Generally, a matrix comes in the shape of a square or rectangle. $$ (1) det(AT) = det(A) But even avoiding these, coming up with one such matrix should be the challenge if you are at a level where you cannot use rotation matrices etc. matrix which is not fully zero) and spanning all the elements, like. At this point I have, $$\pmatrix{a&b\\0&0}\pmatrix{c&0\\d&0}=\pmatrix{ac+bd&0\\0&0}\;,$$. We observe the vectors $(1,1,0)$ and $(1,1,1)$ have the same first two components. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Method 1: Using for loop. Matrix Multiplication - Equality of Row-Column and Column-Row (Strang P71), Matrix Multiplication - Product of [Row or Column Vector] and Matrix [Lay P94, Strang P59], ?-dimensional space involving an m by n and n x 1 matrix (Strang P41 2.1.13), Row and Column Picture of a 3 x 3 Singular Matrix (Strang P43, 2.1.32), Do the vectors not in the column space form a subspace? A: We will use the following properties : Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Most questions answered within 4 hours. and basis Does the Fool say "There is no God" or "No to God" in Psalm 14:1. [Strang P297 6.1.32], What matrix corresponds to the sum of the column space of two matrices? has the property that A2 = 0. Learn more about Stack Overflow the company, and our products. It's just your reasoning about the characteristic polynomial is also not correct. point) Find non-zero_ two-by-two matrix A such that: Now, given any matrix $A$, consider for any invertible matrix $B$, the matrix $B^{-1}AB = C$. Find a change of basis for $\mathbb{R}^3$ such that $P$ is the coordinate matrix from $B$ to the basis $C$. $\Large{1.2}$ You wrote that "taking for $A$ a product will never work." Assume that P is nonsingular and solve this for A. I'd like: $A^2 = \mathbf{c\color{green}{r^Tc}r^T} = \mathbf{0}. How to make use of a 3 band DEM for analysis? notice: A is invertible if and provided that the determinant of A is nonzero. I don't know exactly what you mean by "beget a counterexample"; however (1) a (single column)$\times$(single row) product always has rank at most$~1$, so (2) if $A$ is such a matrix then for any vector $v$, the triplet of vectors $v$, $A\cdot v$ and $A^2\cdot v$ will be linearly dependent, hence (3) in such a situation either $A^2\cdot v=0$ or $A^3\cdot v\neq0$, and finally (4) if $A^3\cdot v=0$ for all $v$ then $A^2\cdot v=0$ for all $v$ as well, so $A$ is not an example of (b) in the question. Why? Step-by-Step Verified Answer This Problem has been solved. But two of the questions we need to prove that every said well, orthogonal article in vectors are linearly linearly independent. a Find the rank and nullity of AB. Can a matrix with zeros on the diagonal have an inverse? Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Theorem 9 on page 213, so no two such solutions can exist. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. rev2023.6.2.43474. Find the projection matrix P onto the plane, and find a nonzero vector b that is projected to zero. Help please. This I expect to be a simple task by experiment : start with some fixed first row of $B$, say $1,2,3$ or something, then find non-zero entries of the second rows so that all cofactors are non-zero, and then do this for the third rows. A [ 1 0 1 0] = 0. A: Here I use excel to solve this problem. If youre comfortable thinking of matrices as linear transformations, you can look for a pair of non-zero linear transformations $S$ and $T$ such that $T\circ S$ sends everything to $0$. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Is there a reliable way to check if a trigger being fired was the result of a DML action from another *specific* trigger? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. It only takes a minute to sign up. We have to simplify the given expression. If it is, determine whether it is in reduced row-echelon form. Two attempts of an if with an "and" are failing: if [ ] -a [ ] , if [[ && ]] Why? Learn more about Stack Overflow the company, and our products. Check out Jordan normal form (if you have not learnt it yet), it decompose any general matrix into block where each is the sum of the shift matrix (as shown in the answer below, either that or shifting in the opposite direction) and a eigenvalue. 2 Solutions [Bretscher, Sec. Find largest row in a matrix with numpy (row with highest length), Python: Find max value along one axis in 3d matrix, make non-max values zero, Find the index of maximum value in numpy exclude zero values. Any suggestions would be greatly appreciated. That's the only non-trivial part of (2). Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Can the use of flaps reduce the steady-state turn radius at a given airspeed and angle of bank? Therefore, our task is to find the unknown matrix X in such a way that, applied to the left-most matrix as a factor from the right, it would produce the zero 2x2-matrix. @FutureMathperson. Living room light switches do not work during warm/hot weather. My method suggests reverse engineering what you would do to simplify. How can I repair this rotted fence post with footing below ground? What does "Welcome to SeaWorld, kid!" Had overlooked that. If I make the second column of $B$ all zeroes, the second column of $AB$ will automatically be all zeroes. The result of this equation is the two-by-two matrix A shown below. answered 11/17/13, Friendly tutor for ALL math and physics courses. A=-300010-180-2 Is there a place where adultery is a crime? Why is it "Gaudeamus igitur, *iuvenes dum* sumus!" Should I include non-technical degree and non-engineering experience in my software engineer CV? mean? (b) Find a matrix that has $A^2 \neq 0$ but $A^3 = 0$. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Find eigenvalues and eigenvectors for a square matrix. How could a person make a concoction smooth enough to drink and inject without access to a blender? Why doesnt SpaceX sell Raptor engines commercially? 5 & 6 & 7 & 8 \\ Find two nonzero matrices A and B such that AB=BA. Short Answer Find a nonzero n n matrix A with identical entries such that A 2 = A. @FutureMathperson - I forced one cell of $A^2$ to be $0$ and then found an easy way to make the others a multiple of it, Form @MarkBennet 's comment, this looks to me as if it may be the general solution. The best answers are voted up and rise to the top, Not the answer you're looking for? Is it OK to pray any five decades of the Rosary or do they have to be in the specific set of mysteries? Connect and share knowledge within a single location that is structured and easy to search. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Then we have to show, A: The given problem is to find the solution for the given heat equation partial differential equation, A: The inverse Laplace transformation formula states thatL-1s-as-a2-b2=eatcoshbt,, A: find a plane throughP2,1,1 and perpendicular to the line of intersection of the planes Why is Bb8 better than Bc7 in this position? You'll get a detailed solution from a subject matter expert that helps you learn core concepts. What if $S$ is the linear transformation that projects the plane to the $x$-axis, and $T$ is the one that projects the plane to the $y$-axis? So pick a row or column of A and make the entries zeros (so, for 0 07 example, start with something like A = or y a 0 TO 01 A= 1). Math Algebra Find a non-zero 2 2 matrix A such that A2 A = Find a non-zero 2 2 matrix A such that A2 A = BUY Elements Of Modern Algebra 8th Edition ISBN: 9781285463230 Author: Gilbert, Linda, Jimmie Publisher: Cengage Learning, expand_more Chapter 1 : Fundamentals expand_more Section: 1.6 Matrices format_list_bulleted Use the fact that A2 to solve for b 0 0 0 the values of the other two entries (you can follow the strategy of the last problem and call them x and y if you like) that will make A2 0 0 [ ] X = [ ] 3). Can I also say: 'ich tut mir leid' instead of 'es tut mir leid'? Is there any philosophical theory behind the concept of object in computer science? Get a free answer to a quick problem. Why is it "Gaudeamus igitur, *iuvenes dum* sumus!" How can I repair this rotted fence post with footing below ground? Diagonalizing selfadjoint operator on core domain. \end{bmatrix} This can be done by solving the equation A2 = 0 for A. Solving a System of Equations without a Square Matrix, Solving a linear system of equations in 3 unknowns, Determining an Elementary 3x3 Matrix E from an Augmented Matrix of a system of Linear Systems, Is there a less time-consuming way to solve a Symmetric Matrix Equation. Manhwa where a girl becomes the villainess, goes to school and befriends the heroine, "I don't like it when it is rainy." ? A: The given matrix is: Is there liablility if Alice scares Bob and Bob damages something? There are no solutions of the form $cr^T$. Can the use of flaps reduce the steady-state turn radius at a given airspeed and angle of bank? This gets the minimum index of np.nonzero as the start range, and the maximum index of np.nonzero as the end range, in both axis. If so, find an example. Snapsolve any problem by taking a picture. My argument shows that you need $A$ to have rank at least$~2$ (as $A\cdot v$ and $A^2\cdot v$ are linearly independent elements of the image of $A$); hence taking for $A$ a product $cr^T$ of a $n\times 1$ and a $1\times n$ matrix will never work. Im waiting for my US passport (am a dual citizen. What are good reasons to create a city/nation in which a government wouldn't let you leave, Movie in which a group of friends are driven to an abandoned warehouse full of vampires, Cartoon series about a world-saving agent, who is an Indiana Jones and James Bond mixture. It only takes a minute to sign up. $. For an easy example, take the (sub)space generated by $v,A\cdot v,A^2\cdot v$. The expected result in the question is incorrect. Orthogonal Vectors in $\Bbb R^n$ where $n>3$. Living room light switches do not work during warm/hot weather. First, Id look for a simple example, so Id start with $2\times 2$ matrices, say $A$ and $B$. Creating knurl on certain faces using geometry nodes. Because all vectors were previously projected into the rotated line, everything gets mapped into zero on the second run. That is, all we need to do is to ensure that the determinant, all cofactors and all entries of $B$ are non-zero. Therefore it is guaranteed to include all non-zero elements. How appropriate is it to post a tweet saying that I am looking for postdoc positions? This can be done by simple trial and error, and will give you a matrix $B$ such that $B^{-1} DB$ has non-zero entries. Is there a faster algorithm for max(ctz(x), ctz(y))? In any respect, I'll return here later. How common is it to take off from a taxiway. You need a vector that is perpendicular to the plane; i.e. how to determine singular matrix using qr. thanks. a^2 + bc = 0 \\ Solution for (a): Let A := column row = c r T 0 where c, r are column vectors. You want there to be a vector $v$ with $A^2\cdot v\neq0$ but $A^3\cdot v=0$. We want A^2 to be the zero matrix, so: $\alpha 3 \times 1,\beta' 1 \times 3$,so $\alpha \beta'$ IS $3 \times 3$. So pick a row or column of A and make the entries zeros (so, for 0 07 example, start with something like A = or y a 0 TO 01 A= 1). Since my textbook presents "rank" but far after this question, is it possible to answer without "rank"? Finding the maximum row with all elements not zero, max of a column in a numpy array in python, Finding largest indices of non-zero elements along each axis. Connect and share knowledge within a single location that is structured and easy to search. Find two nonzero matrices A and B such that AB=BA. A2. A 1 0 1 0 = 0. Why do some images depict the same constellations differently? You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Should convert 'k' and 't' sounds to 'g' and 'd' sounds when they follow 's' in a word for pronunciation? How to find the basis of the following vector space? Upvote 1 Downvote Add comment Report Andre W. answered 11/17/13 Tutor 5 (3) Friendly tutor for ALL math and physics courses Find the projection of a vector on a subspace. b Show that matrices A and B must be identical. Thus, for want of a counterexample, choose r = ( 0, k) and c = ( k, 0) T. Does the Fool say "There is no God" or "No to God" in Psalm 14:1. CEO Update: Paving the road forward with AI and community at the center, Building a safer community: Announcing our new Code of Conduct, AI/ML Tool examples part 3 - Title-Drafting Assistant, We are graduating the updated button styling for vote arrows, a matrice that becomes zero when multiplied with its factor, a mathematical object that becomes zero when squared. AI Recommended Answer: The first step is to identify the two-by-two matrix A such that A2 = 0. VS "I don't like it raining.". Compute the characteristic equation 3x3 matrix, Construct a basis of the matrix elements in the space $\mathbb{C}[S_{3}]$. Is there a faster algorithm for max(ctz(x), ctz(y))? p1=1p2=1+xp3=1+x+x2, A: Given expression isaaaccc. My question: I know that if A is an n n matrix with all the diagonal elements and all the elements below it equal to zero then A n = 0, so in this question ( 0 x 0 0) qualifies as A, but it does not agree with b = c as in above solution, so where did I go wrong? 1 Expert Answer Best Newest Oldest Raymond B. answered 10/12/22 Tutor 5 (2) Math, microeconomics or criminal justice See tutors like this 7a-6c = 0 -14a +12c = 0 the two equations are linearly dependent with an infinite number of solutions same with 7b-6d = 0 -14b+12c= 0 a=6, c=7 b=6, d=7 is one solution 6 6 7 7 another is a=12=b c=14=d 12 12 What is the maximum rank of a 53 matrix? Table generation error: ! the number of vehicles leaving this area during this hour was exactly the same as the of vehicles entering it. CEO Update: Paving the road forward with AI and community at the center, Building a safer community: Announcing our new Code of Conduct, AI/ML Tool examples part 3 - Title-Drafting Assistant, We are graduating the updated button styling for vote arrows, Linear Algebra. I ve come up with this for now. Other than just applying formulas, do you understand the meanings of these words? To learn more, see our tips on writing great answers. Is Spider-Man the only Marvel character that has been represented as multiple non-human characters? It only takes a minute to sign up. At this point I have How to make use of a 3 band DEM for analysis? There's an idea. \end{bmatrix} Learn more about Stack Overflow the company, and our products. 0 2 1 2 1 1 3 2 0 01 The. Whilst I could in theory solve that, is there more intuitive way of solving this problem or am I going to have to brute force the solution? So, the matrix (1) is your ANSWER . Suppose A =0 and A=[acbd], then A=0 and A 2(a+d)A+adbc=0 a+d=0 tr(A)=0 Hence, option B. Note: this doesn't necessarily help you solve your problem; see the answers below. If you project your space onto a line $\ell$ and then rotate this line by $90^\circ$ degree, all vectors are now orthogonal to the line $\ell$. So we need to find a non zero matrix of order three. rank(A) 0 with. An eigenvector of A is a nonzero vector v in R n such that Av = v , for some scalar . For example, here are two matrices that multiply to zero, despite having all non-zero entries: $\begin{bmatrix} Think about a matrix $P$ which orthogonally projects all of $\Bbb R^3$ onto a one-dimensional subspace spanned by a vector $n$: After projection, rotate your space by $90^\circ$ around some axes $v$ orthogonal to $n$ by using a rotation matrix $R$. A: This is the question of LPP and optimization. The matrix of $A$ on this basis will be See Answer Question: (a) Find an example of a nonzero 3 3 matrix A such that A2-0. mean? How to find a matrix that when multiplied with its transpose, creates a known PSD matrix? 1024011130000. Asking for help, clarification, or responding to other answers. The best answers are voted up and rise to the top, Not the answer you're looking for? How do you figure out if a matrix is invertible? The best answers are voted up and rise to the top, Not the answer you're looking for? \begin{pmatrix} A more systematic approach would be to start with a general 2x2 matrix, A=[[a,b],[c,d]], the square it, set A=0, and see what conditions you get for a, b, c, and d. You find that the diagonal elements a=d=0, and bc=0, so only one off-diagonal element can be non-zero. -5& -10& -15 Connect and share knowledge within a single location that is structured and easy to search. (a) Find a nonzero matrix $A$ for which $A^2 = 0$. If you choose appropriate $n$ and $v$, your matrix will not have zero-entries. If you fall asleep in the second room, you have a 50% chance of waking up in the first room, otherwise you disappear. In mathematics, various functions can be carried out with matrices. $$ M = \begin{bmatrix} 0 & 0 & 0 \\ \frac 12 & 0 & 0 \\ \frac 13 & \frac 13 & 0 \end{bmatrix} $$ This meets the requirements in the question. We can try to put $A = \alpha \beta'$, where $\alpha,\beta$ are $3 \times 1$ matrix. Hahn-Banach Theorem, A: given (2) det(AB) = det(A) det(B) Choose an expert and meet online. If not doable, please tell me). See Answer Question: Find a non-zero 2 x 2 matrix A such that A2 0 0 A= E = Hint: A cannot have ALL entries be zeros according to the instructions, but you CAN let one whole row or one whole column be all zeros to make calculations easier. a Question A: The representation of the above equation in matrix form is in the image below. Find the projection matrix P onto the plane, and find a nonzero vector $b$ that is projected to zero. This problem has been solved! I found the matrix $P$ as shown below, but I can't figure out how to find a nonzero vector $b$, I found only the zero vector, help me out? f(x, y) = x2 + y2 How did you reach this conclusion? I need to find the projection of a vector onto the plane perpendicular to some other vector. We know that, A: Let's take first class tickets as x, where x>25 1 \\ 1 \\ -2 \end{pmatrix}$, and $A = \begin{pmatrix} 1 & 1 & -2 \\ 1 & 1 & -2 \\ 1 & 1 & -2 \end{pmatrix}$, Force the first element of $A^2$ to be $0$, for example by finding $b,c,d,e$ with $bd+ce \lt 0$ and let $a=\pm{\sqrt{-(bd+ce)}}$, \begin{bmatrix}a&b&c\\d&db/a&dc/a\\e&eb/a&ec/a\end{bmatrix}. Also, could you please explain Q2 (now enumerated in my OP)? Ways to find a safe route on flooded roads. 3 First, I'd look for a simple example, so I'd start with 2 2 matrices, say A and B. is the simplest example of such a matrix. A link to the app was sent to your phone. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Linear dependence lemma - non-zero vector, Assured non-zero orthogonal projection of a vector. I have to use solely the properties of inverses, rank and inverses. #1 Find a nonzero 2 x 2 matrix A such that AA has all zero entries renegade05 Full Member Joined Sep 10, 2010 Messages 260 Nov 30, 2011 #2 What you speak of is called a nilpotent matrix. For Free. How to determine whether a set is a vector space or not? which provides your example. First week only $4.99! A, Find a non-zero 2 2 matrix A such that A2 A =, Elementary Linear Algebra (MindTap Course List), Algebra & Trigonometry with Analytic Geometry. Could entrained air be used to increase rocket efficiency, like a bypass fan? 0 0 Similar questions If A is a 33 skew-symmetric matrix, then trace of A is equal to Medium View solution > The matrix B is Hard The same procedure can be applied to 3X3 matrices as well. PLEASE HELP!!! So, this is fun question to evaluate a matrix from it's general form when a set of conditions are applied to it. You find yourself in a house with 3 rooms and no doors. 1 asked Oct 23, 2014 at 3:49 Empty 12.7k 7 41 106 If A has a nonzero eigenvalue, can A 2 possibly be zero? [GStrang P191 3.6.6], If two matrices have the same 4 fundamental subspaces, then free variable submatrices must be equal. Let A =\begin {bmatrix} -9 & -0.25\\ 288 & 9 \end {bmatrix}. Insufficient travel insurance to cover the massive medical expenses for a visitor to US? If not, prove why not. Is it possible? Therefore, A 1 = P 1 1 D 1P 1 = PD 1P 1; and A 1 is also diagonalizable with the same . First story of aliens pretending to be humans especially a "human" family (like Coneheads) that is trying to fit in, maybe for a long time? How does TeX know whether to eat this space if its catcode is about to change? To attain moksha, must you be born as a Hindu. However, if two similar matrices are diagonalizable, the task becomes easier. Making statements based on opinion; back them up with references or personal experience. Get Started Already have an account? when you have Vim mapped to always print two? ab + bd = 0 \\ Would the presence of superhumans necessarily lead to giving them authority? Let A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}. If you fall asleep in the first room, you disappear. For the row space, pick any (nonzero) row. mean? }$ Could someone please reveal and expound on the intermediate steps and thoughts towards devising a (counterexample) for $A^3$? 3& 6& 9&\\ VS "I don't like it raining.". -2 & 1 & 4 & -1 \\ arrow_forward. What does Bell mean by polarization of spin state? Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. = If I make the second column of B all zeroes, the second column of A B will automatically be all zeroes. What does "Welcome to SeaWorld, kid!" If you fall asleep in the third room, you have a 33% chance of waking up in the first room, 33% chance of waking up in the second room, otherwise you disappear. If I make the bottom row of $A$ all zeroes, the bottom row of $AB$ will automatically be all zeroes. Can the use of flaps reduce the steady-state turn radius at a given airspeed and angle of bank? Find a non-zero 2 x 2 matrix A such that A2 0 0 A= E = Hint: A cannot have ALL entries be zeros according to the instructions, but you CAN let one whole row or one whole column be all zeros to make calculations easier. CEO Update: Paving the road forward with AI and community at the center, Building a safer community: Announcing our new Code of Conduct, AI/ML Tool examples part 3 - Title-Drafting Assistant, We are graduating the updated button styling for vote arrows. A nonzero n n matrix A with identical entries such that A 2 = A is A = 1 n 1 n 1 n 1 n n n See the step by step solution Step by Step Solution TABLE OF CONTENTS Step 1: Definition of Idempotent matrix Spectral Theory refers to the study of eigenvalues and eigenvectors of a matrix. Is there a faster algorithm for max(ctz(x), ctz(y))? Why the answer is that instead of 4x4 matrix with all 0 except for the top-left element, which is 4? Now, We will check that, AB = 0 or not Hence, A = [ 1 0 0 0] [ 1 0 0 0] and B =[ 0 0 0 1] [ 0 0 0 1] are the two non - zero matrices such that AB = 0. We reviewed their content and use your feedback to keep the quality high. $$ I found the matrix P as shown below, but I can't figure out how to find a nonzero vector b, I found only the zero vector, help me out? Therefore it is guaranteed to include all non-zero elements You'll get a detailed solution from a subject matter expert that helps you learn core concepts. = In + 3B. I'm not supposed to use eigenvectectors, rotations or diagonolizaton. This problem has been solved! Note that once $a,b,c,d,e$ are fixed the other entries are determined by the rank $1$ condition and the $A^2=0$ condition implies that $a^2+bd+ce=0$. Solved. Then find an invertible matrix P such that . Hint: apply A 2 to the corresponding eigenvector. Is it possible to type a single quote/paren/etc. Find two nonzero matrices and such that. Find two nonzero matrices A and B such that AB=BA. I'm not sure, Finding the maximum non-zero matrix in python, Building a safer community: Announcing our new Code of Conduct, Balancing a PhD program with a startup career (Ep. It is about making intelligent choices. Allowable stress for concrete co= 6, A: Given A: Given Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. And if I go with b = c, then A 2 does not equal 0. linear-algebra matrices Share Cite This will not change the result. To be extremely fair, I am still looking for a simpler way than trial and error to get a matrix of the kind I mentioned. Get 5 free video unlocks on our app with code GOMOBILE. Look up. Is there any philosophical theory behind the concept of object in computer science? Find a matrix so that $A^2$ not equal to 0 but $A^3$ is [Strang P78 2.4.23], CEO Update: Paving the road forward with AI and community at the center, Building a safer community: Announcing our new Code of Conduct, AI/ML Tool examples part 3 - Title-Drafting Assistant, We are graduating the updated button styling for vote arrows.

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