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Math / Linear Algebra with Applications 9 / Chapter 1 / Problem 1

Linear Algebra with Applications | 9th Edition | ISBN: 9780321962218 | Authors: Steven J. Leon

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Use MATLAB to generate random 44 matrices A and B. For each of the following, compute

Chapter 1, Problem 1

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QUESTION:

Use MATLAB to generate random 44 matrices A and B. For each of the following, compute A1, A2, A3, and A4 as indicated and determine which of the matrices are equal (you can use MATLAB to test whether two matrices are equal by computing their difference). (a) A1 = A B, A2 = B A, A3 = (A B ) , A4 = (B A ) (b) A1 = A B , A2 = (A B) , A3 = B A , A4 = (B A) (c) A1 = inv(A B), A2 = inv(A) inv(B), A3 = inv(B A), A4 = inv(B) inv(A) (d) A1 = inv((A B) ), A2 = inv(A B ), A3 = inv(A ) inv(B ), A4 = (inv(A) inv(B))

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QUESTION:

Use MATLAB to generate random 44 matrices A and B. For each of the following, compute A1, A2, A3, and A4 as indicated and determine which of the matrices are equal (you can use MATLAB to test whether two matrices are equal by computing their difference). (a) A1 = A B, A2 = B A, A3 = (A B ) , A4 = (B A ) (b) A1 = A B , A2 = (A B) , A3 = B A , A4 = (B A) (c) A1 = inv(A B), A2 = inv(A) inv(B), A3 = inv(B A), A4 = inv(B) inv(A) (d) A1 = inv((A B) ), A2 = inv(A B ), A3 = inv(A ) inv(B ), A4 = (inv(A) inv(B))

ANSWER:

Step 1 of 4

Let us consider two matrices and defined by

Given

The MATLAB code for generating the above matrices is given below.

By running the MATLAB code, it is determined that

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