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Or you can type in the big output area and press "to A" or "to B" (the calculator will try its best to interpret your data). A= (1&5 &6 \\ 2&-4 & 0), B = ( 7& 5& 2\\ 0& 1& 0), Finding the Product of Two Matrices . (1) Write down your matrix B B as a matrix of unknowns. Then, A ( c 1 B + c 2 C) = c 1 A B + c 2 A C = c 1 B A + c 2 C A = ( c 1 B + c 2 C) A. c) Find \mathrm{adj}(A) . x 0 3 0 0 2 ? Find AB and AB+C from the following matrices, Find the following for the given matrix A. Or (2) If matrix A A is invertible, use its inverse. A = ((10 5 3), (11 2 4), (11 4 41)), B = ((0 2 3), (15 9 6), (5 6 7)). If B = `[(-4, 2),(5, -1)] and "C" = [(17, -1),(47, -13)]` find the matrix A such that AB = C, Then AB = `[(a, b),(c, d)] xx [(-4, 2),(5, -1)]`, = `[(-4a + 5b, 2a - b),(-4c + 5d, 2c - d)]` AB = C. `[(-4a + 5b, 2a - b),(-4c + 5d, 2c - d)] = [(17, -1),(47, 13)]`Comparing corresponding elements, we get 4a + 5b = 17 .(i)2a b = 1 .(ii)4c + 5d = 47 .(iii)2c d = 13 .(iv)Multiplying (i) by 1 and (ii) by 2 4a + 5b = 17 4a 2b = 2Adding3b = 15 b = `(15)/(3)` = 52a b = 1 2a 5 = 1 2a = 1 + 5 = 4 a = `(4)/(2) + 2` a = 2, b = 5Again multiplying (iii) by 1 and (iv) by 2,4c + 5d = 474c 2d = 26Adding3d = 21 d = `(21)/(3)` = 7and2c d = 13 2c 7 = 13 2c = 13 + 7 = 6 c = `(-6)/(2)` = 3 c = 3, d = 7Now matrix A = `[(2, 5),(-3, 7)]`. All rights reserved. Createyouraccount, We are given a matrix {eq}\mathbf A if matrix E and F are 2x2 matrices and given det(E) = 1, det(F) = -5, How do you find something like det(EF 1 E T )? How do you find the determinant of a 4x4 matrix? Finding the Product of Two Matrices. x ? And the task is to find a matrix B such that A*B is the identity matrix. The matrix multiplication provides a new matrix. How would I solve this? . Perform the given matrix operation. 1. Answers and Replies Feb 14, 2007 #2 d_leet 1,077 1 copyright 2003-2023 Homework.Study.com. Given a matrix A , how do you determine if this matrix is invertible? (take any matrix A and B as example), Let A = 0 & -1 & 0 0 & 1 & 0 -3 &-1 & 1 and B = 1& 0 & -2 -1 & 2 & 0 1 &-1 & 0 a) Compute A^{-1} b) Find a matrix C such that AB^{-1} = I_3. Find the matrix product AB, if it is defined. What is A^{-1} ( The inverse of the matrix) using matrix properties? Find: Suppose that A is an m\times k matrix and B is a k \times n Show that (AB)'= B'A' Show that AC \neq CA. Find the matrix product AB, if it is defined. How to find the determinant of 4 tims 4 matrix? You'll get a detailed solution from a subject matter expert that helps you learn core concepts. ? If A = \begin{bmatrix} 8 & 2 & -2\\ 2 & 5 & 4\\ -2 & 4 & 5 \end{bmatrix}, find: (i) trace(A), det(A) (ii) a matrix P that diagonalizes the matrix A if A is diagonalizable (iii) a diagonal matrix D which is similar to matrix A, Given matrices A = \begin{bmatrix} 1&1 \\ 1&2 \end{bmatrix} and B = \begin{bmatrix} 2&-1 \\ -1&1 \end{bmatrix}. (This is similar to the restriction on adding vectors, namely, only vectors from the same space R n can be added; you cannot add a 2vector to a 3vector, for example.) A=[., 11] c=(-1 (Note: The textbook's version of this problem was solved on The Finite Show. Find all possible $2 \times 2$ matrices A that for any $2 \times 2$ matrix B, AB = BA. Find the following for the given matrix . a. Find the determinant of the matrix A. {/eq} with size m x n and a matrix {eq}\mathbf B a 1,3 is the value of the element in the first row and the third column of the given matrix. ? Find the determinant of the matrix. d) Find A^{ 1} . We can add (or subtract) two matrices only if they have the same ______. How do you find the determinant of a 4x4 matrix recursively? \displaystyle A = \begin{bmatrix} 2 & 1 &-1 \\ 4 & 7 & -2\\ 2 & 4 & 0 \end{bmatrix}. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site b) Find the matrix of cofactors C . Mathematics Linear and Abstract Algebra How to make a matrix B such that AB=BA yooyo Feb 14, 2007 Matrix 1 2 Next Feb 14, 2007 #1 yooyo 7 0 B is not the identity matrix or the zero matrix suppose both A and B are 3X3 I don't have clue on this..any hits? Find the matrix product AB. Find the matrix that represents B - A? Find two nonzero matrices and such that. 2003-2023 Chegg Inc. All rights reserved. A = \begin{bmatrix} 3&-2 & 4 \\ 6 &1 & 0 \\ -5 & 9 & 5 \end {bmatix}, B = \begin{bmatrix} 1&5 & 0 \\ 4 &4 & 7 \\ 2 & 3 & -9 \end {bmatix} i. D) Find the inverse of the matrix, Find the values of the variables. How do you find the determinant of a triangular matrix? [8 5;2 -4], Find the determinant of the matrix A= -5 10 1 10. [2 8 0 -1 7 2 -1 5]. {/eq} is found by left Our experts can answer your tough homework and study questions. Example: Enter The matrix TO FIND : The matrix B such that AB=I SOLUTION : Given that the matrix is Now we have to find the matrix B such that AB=I We know that the Identity Matrix for 2x2 matrix is given by Substitute the matrices in the equation AB=I we get AB=I The formula for is Now find |A|: =6-4 |A|=2 Now in we have that the matrix B is Advertisement How to find a^10 matrix when the matrix a is given? Let B be the matrix \begin{pmatrix} 0 & 2 & 1 & 1 \\ 1 & 0 &-1 & 0\\ 0 & 1 & 0 & 1\\ 2 & 3 & 9 & 1 \end{pmatrix} Find the determinant of the matrix (2B^{3}) (B^{T})(B^{-1})^{2}. A where A is multiplied by itself A times. AB A = \begin{bmatrix} 1 & 2 & 3\\ 2 & 4 & 6\\ 3 & 6 & 9 \end{bmatrix} \;\;\; B = \begin{bmatrix} -1 & -1 & -1\\ -1 & -1 & -1\\ 1 & 1 & 1 \end{bmatrix}, Find the matrix X if 3 & 1 -1 & 4 X = 4 & 2 1 & 3, Matrice A is 1 \times 1 and B is 1 \times 1. Let A = \left[ \begin{array}{lr} 5e^{4t} & 4e^{5t} \\ 6e^{4t} & 5e^{5t} \end{array} \right] . Let A be a 4 by 9 matrix, B be a 9 by 6 matrix, and C be a 6 by 4 matrix. Given the matrix: A = (4 8 6, 2 -4 -4, -6 6 4). A=2x2 matrix, B= 2x2 matrix. Find the transpose of the matrix. How to find the transformation matrix between two matrices? See Answer ? Hint: AB = BA must hold for all B. Find a matrix A. Question: (1 point) Rework problem 35 from section 6.1 of your text, involving finding a matrix B such that AB = C. Use the following matrices instead of those found in your book. Find AB, if possible. A + B A - B AB A B: A matrix, in a mathematical context, is a rectangular array of numbers, symbols, or expressions that are arranged in rows and columns. Find the determinant of each matrix then find AB. Find an LU-Decomposition of.the matrix A = \begin{bmatrix} 2& 1& -1\\ -2& 1& 2\\ 2& 1& 0\end{bmatrix}. Solve the system AX = \begin{bmatrix} 0 \\ 3 \\ 2 \end{bmatrix}. a.\ A= \begin{bmatrix} 1 & 2 & -1\\ 3 & 4 & 0\\ 2 & 5 & 1\end{bmatrix},\ B = \begin{bmatrix} 4 & 6 & -2\\ 7 & 2 & 1\\ -1 & 0 & 0 \end{bmatrix}\\ b.\ A= \begin{bmatrix} 1 &. A = (1 0, 0 2), B = (1 2 -2, 2 -2 2). x 0 3 0 1 2 ? Share Cite Follow answered Sep 28, 2014 at 11:06 As Alex Becker said, we could use any scalar multiple of I or A n where A n = A A . ? Find the determinant of the matrix. ? (1 point) Rework problem 35 from section 6.1 of your text, involving finding a matrix B such that AB = C. Use the following matrices instead of those found in your book. Let A = \begin{bmatrix} 3 &1\\ -1&0 \end{bmatrix} and B = \begin{bmatrix} 2&7\\ 6&4\\ 1&6 \end{bmatrix}. Consider the matrix A = (5 -2, 4, -2). 8 4 2 3, Find the determinant of the 3 times 3 matrix below: -2 3 1 2 -1 -1 4 0 2. Find the transpose of the given matrix. Find AB and BA. Become a Study.com member to unlock this answer! How to determine if matrix is invertible? Use hte results in i), to find c_{23}, Find the determinant of A + B Matrix A : \begin{bmatrix} -3&1 4&-8 \end{bmatrix} Matrix B : \begin{bmatrix} 12&8 -1&-5 \end{bmatrix} -117 -144 68 -28. Statistics and Probability questions and answers. Find all values of c, if any, for which the given matrix is invertible. Enter your matrix in the cells below "A" or "B". 9 ], If you are asked to find (AB) transpose without computing AB, how would you do that? ? Find the matrix product AB, if it is defined. Given the following matrices A=1X2 matrix and B=2x1 matrix, compute A*B. Can you find determinant of a 2x3 matrix? Matrix operations such as addition, multiplication, subtraction, etc., are similar to . Find the determinant of the matrix. Find the matrix product AB, if it is defined. Understand what a matrix is in math, how proper matrix notation is written, and what is matrix order. How to find the determinant of the 5x5 matrix? 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Given the following matrices A=1X2 matrix and B=2x1 matrix, compute A*B. If A and B are matrices of the same size, then they can be added. How do you find the determinant of a 3x4 matrix? You can view the streaming video of this solution at TFS solution. A = ? \begin{bmatrix} 1 & -2 &3 &1 \\, Find the determinant of the matrix A. Find the value of the determinant of the matrix (-1 1 0 0 2 -2 -1 1 0). Hint: Let B = a b c d . 2. {/eq}. Find the determinant of the matrix. I'm clueless as to how to solve this problem. Find AB, if possible. Find two nonzero matrices A and B such that AB=BA. . In this exercise we know that the determinant of the 2 by 2 matrix A is not zero. Find: If Matrix A= \left [B + C + D + E \right ]. Find AB and AB+C from the following matrices. How to find the determinant of a 4\times{4} matrix? Experts are tested by Chegg as specialists in their subject area. A=2x3 matrix, B= 2x2 matrix. Solution B = [ - 4 2 5 - 1] C = [ 17 - 1 47 - 13] and AB = C Let A = [ a b c d] Then AB = [ a b c d] [ - 4 2 5 - 1] = [ - 4 a + 5 b 2 a - b - 4 c + 5 d 2 c - d] AB = C [ - 4 a + 5 b 2 a - b - 4 c + 5 d 2 c - d] = [ 17 - 1 47 13] Comparing corresponding elements, we get -4a + 5b = 17 .. (i) 2a - b = -1 .. (ii) -4c + 5d = 47 .. (iii) If A and B are matrices such that AB and BA are defined (can be multiplied) ABBA. Find C=2B+A-2I where I is the identity matrix. Matrix addition. Find the values of x so that the following matrix is invertible. {/eq} and the matrix product {eq}\mathbf {AB}. \begin{bmatrix} 10&6&6&-9\\7&1&-12&8 \end{bmatrix}, Find the determinant of the matrix if this matrix invertible? A = ( 6& 5& 7), B =( -1 \\ 4 \\ 8 ). How to find matrix b given matrix ab and a? #1 lubricarret 34 0 Homework Statement Let A= [-1 4 3 -12] Find two 2x2 matrices B and C such that AB=AC but B does not equal C . The matrix {eq}\mathbf B Try matrices B that have lots of zero entries. Find the following from the given matrix A. It is given that and and In teh identity above pre multiplyi. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Given matrices A and B. b. How to find the determinant of an n\times{n} matrix? {/eq} with size n x q. Find 2 matrices that when multiplied = 0. How to find the determinant of a block matrix? Find the matrix product AB. This problem has been solved! Find the matrix product AB, if it is defined. I tried plugging in values for B that "have lots of zero entries" but didn't seem to see anything that could . If A = (1 6 3 4 2 1), B = (2 0 3 5 4 1-3 1 7) find the size of the matrix C where C = AB. Find the matrix product AB, if it is defined. 3 0 4 0 5 0 1 0 7 ). 1 -6 7 4 0 -8 -2 4 5, Find the determinant of the matrix. Find B. For the given matrix A, find the following. If any. A=2x2 matrix, B= 2x2 matrix. Find all matrices B such that A B = B A Since we want to find B such that A B = B A, we need to find x, y, z, w satisfying [ 1 3 2 4] [ x y z w] = [ x y z w] [ 1 3 2 4]. A = (1 0, 0 2), B = (1 2 -2, 2 -2 2). You can view the streaming video of this solution at TFS solution. = [:] B= This problem has been solved! Let A := ( 1 3 0 2 ) B := ( 2 2 1 5 ) Find a 2 2 matrix X for which the following matrix equation is satisfied: A X B = A T B 1 + A B. See Answer x 0 0 0 1 2 ? How do you find the determinant of a 5x5 matrix? We could also use A 1 or ( A 1) n. Suppose we have any matrices B and C that satisfy A B = B A and A C = C A. Algebra Algebra questions and answers (1 point) Suppose 8 -31 A= -24 9 Find a non-zero 2 x 2 matrix B, such that AB equals the 2 x 2 zero matrix. x + 3 z = x + 2 y y + 3 w = 3 x + 4 y 2 x + 4 z = z + 2 w 2 y + 4 w = 3 z + 4 w. Find a matrix B such that AB = I, where A = 6 1 6 6 and I = 1 0 This problem has been solved! -7 6 1/2 3, Find the determinant of the following matrix. How should I start it? ? Let us consider two matrices {eq}\mathbf A Show that no 22 matrices A and B exist that satisfy the matrix equation. Using examples of matrices, learn about equal matrices and matrix math operations. 3 -3 4 -8. If it is, find the matrix that diagonalizes it. {/eq} with size m x q. How to find the determinant of a 3x3 matrix? How do you find the determinant of a square matrix? Find a matrix B such that AB = I, where A = 6 1 6 6 and I = 1 0 1. Find a matrix that when multiplied by another matrix gives zero. It is found that right-multiplication by D multiplies each column of A by the corresponding diagonal entry of D, whereas left-multiplication by D multiplies each row of A by the corresponding diagonal entry of D. Construct a 3 x 3 matrix B, not the identity matrix or zero matrix, such that AB = BA A B = B A. linear-algebra matrices Share Cite Find the determinant of the matrix. A = (1&3 &2 \\ 0 & 2& -4\\ 1& -1& 3), B = (4&-3 &2 \\ 0&3 &-1 \\ 0& 6&2), Finding the Product of Two Matrices. Find AB, if possible. a) Calculate M^-1. Find the a d j n o i n t matrix of A = [ ? See Answer Question: 1. Find 2\times 2 matrices A and B such that AB equals 0 but BA does not equals to 0. b) Find the matrix C such that MC = B. How do you find the determinant of a diagonal matrix? Solution 2. Let M = (1 -2 1 -3 7 -6 2 -3 0) and B = (1 2 -3 2 5 6). A) Find the transpose of the matrix A. Then do the matrix multiplication of A A and B B and equate it to the known AB A B, giving you a system of equations to solve. B) Find the cofactor of the element 2. Get access to this video and our entire Q&A library, Matrix Notation, Equal Matrices & Math Operations with Matrices. How to find the determinant of a 7x7 matrix? Matrix a+10 10z+1 7m 11k 3 4 + matrix 4a 3z 7m 3k 5 2 = matrix 25 -25 140 14 8 6, For each pair of matrices, find the (1,2)-entry and (2,3)-entry of the product AB. How to find the inner product of matrices? (-1 3 4, -2 8 0, 2 5 -1). Advanced Math Advanced Math questions and answers Find a matrix B such that AB = I, where A = 3 1 3 3 and I = 1 0 0 1 . 3 14 5 ? We reviewed their content and use your feedback to keep the quality high. If A^{-1} = \begin{bmatrix} 2 & 0 & 0 \\ -3 & 6 & 0 \\ 2 & 4 & -2 \end{bmatrix}: 1. How do you find the elementary matrix for a non-square matrix? ii. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Determine the size of the following matrix: AB. 3. 11. Can you find the determinant of a 3x4 matrix? \begin{bmatrix} 5 & 6 & -1 \\ -7 & 6 & 6\\ -3 & 1 & 1 \end{bmatrix}. Can you find 2x2 matrices A and B such that AB is the zero matrix, but neither A nor B are the zero matrix? ? You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA. Check the very first property listed here: . Homework Equations The Attempt at a Solution I was going through my book, and am a bit confused with this problem. Find A^{-1}. {eq}\mathbf C = \mathbf {AB} How do you find the rank of a matrix using its determinant? C) Find the determinant of the matrix A. A=[., 11] c=(-1 (Note: The textbook's version of this problem was solved on The Finite Show. A=2x3 matrix, B= 3x2 matrix. a) Find \mathrm{det}(A) . Find AB. 2 ? All other trademarks and copyrights are the property of their respective owners. Find all values of a, if any, for which the given matrix is invertible. i m a bit doubtful about the second option for instance if I 2 is a 2 * 2 matrix and A is 2*3 while B is 3*4 well then AB would be 2*4 so I2 ( AB) would be defined but (AB) I2 wouldnt be possible. Determine whether or not the matrix below is diagonalizable. Comparing entries, we have the following system of linear equations. Compute AB and 2A-3B for the following matrices A and B. A = \begin{bmatrix} 7 & 4\\ 2 & -3\\ -9 & -8 \end{bmatrix}\;\;\; B = \begin{bmatrix} -5 & 6\\ 1 & -10\\ 0 & -1 \end{bmatrix}, Find the determinant of the matrix A defined below: A = (2 0 5 0 1 1 -2 4 3), Find the determinant of the matrix A defined below: A = 2 0 1 3 1 1 1 1 0, Find the determinant of the matrix: [-1/2 1/3 -30 1/3], Find the determinant of the matrix. (3,1,2,-1,1,0,0.2.1). How do you find the determinant of a 2x3 matrix? \begin{bmatrix} c & 1 & 0\\ 1 & c & 1\\ 0 & 1 & c \end{bmatrix}. Find the determinant of A + B, where A and B are given matrices? Suppose there is a matrix B such that AB = (1 -4, 2 -6). Solution.

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