Explanation Approach: Two matrices A and B can be multiplied if they satisfy the condition that the number of columns in A is same as the number of rows in B . If A is a square matrix of dimension n × n and there exist another square matrix B of dimension n × n such that A B = I = B A , then B is the inverse of A . Calculation: A B = [ 2 − 1 3 2 − 2 1 0 1 1 ] [ − 3 2 2 5 2 − 1 1 2 1 − 1 − 1 ] = [ 2 ( − 3 2 ) + ( − 1 ) ( − 1 ) + 3 ⋅ 1 2 ⋅ 2 + ( − 1 ) 1 + 3 ( − 1 ) 2 ⋅ 5 2 + ( − 1 ) 2 + 3 ( − 1 ) 2 ( − 3 2 ) + ( − 2 ) ( − 1 ) + 1 ⋅ 1 2 ⋅ 2 + ( − 2 ) 1 + 1 ( − 1 ) 2 ⋅ 5 2 + ( − 2 ) 2 + 1 ( − 1 ) 0 ( − 3 2 ) + 1 ( − 1 ) + 1 ⋅ 1 0 ⋅ 2 + 1 ⋅ 1 + 1 ( − 1 ) 0 ⋅ 5 2 + 1 ⋅ 2 + 1 ( − 1 ) ] = [ − 3 + 1 + 3 4 − 1 − 3 5 − 2 − 3 − 3 + 2 + 1 4 − 2 − 1 5 − 4 − 1 0 − 1 + 1 0 + 1 − 1 0 + 2 − 1 ] = [ 1 0 0 0 1 0 0 0 1 ] = I And,

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 11.CR, Problem 46E

To determine

To Find:

The products AB and BA and hence verify that the given matrices A=[2−132−21011] and B=[−32252−1121−1−1] are inverses of each other.

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Chapter 11 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 11.1 - If a system of linear equations has infinitely...Ch. 11.1 - Write the augmented matrix of the following system...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - 5-10 Dimension of a Matrix State the dimension of...Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The products A B and B A and hence verify that the given matrices A = [ 2 − 1 3 2 − 2 1 0 1 1 ] and B = [ − 3 2 2 5 2 − 1 1 2 1 − 1 − 1 ] are inverses of each other.

Solution Summary: The author explains that two matrices A and B can be multiplied if they satisfy the condition that the number of columns is the same.

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To Find:

The products AB and BA and hence verify that the given matrices A=[2−132−21011] and B=[−32252−1121−1−1] are inverses of each other.

Chapter 11 Solutions

The products A B and B A and hence verify that the given matrices A = [ 2 − 1 3 2 − 2 1 0 1 1 ] and B = [ − 3 2 2 5 2 − 1 1 2 1 − 1 − 1 ] are inverses of each other.

Solution Summary: The author explains that two matrices A and B can be multiplied if they satisfy the condition that the number of columns is the same.

Videos

To Find: The products AB and BA and hence verify that the given matrices A=[2−132−21011] and B=[−32252−1121−1−1] are inverses of each other.

Chapter 11 Solutions

To Find:

The products AB and BA and hence verify that the given matrices A=[2−132−21011] and B=[−32252−1121−1−1] are inverses of each other.