Explanation Given information: The matrix A is [ 2 − 1 3 2 − 2 1 0 1 1 ] . The matrix B is [ − 3 2 2 5 2 − 1 1 2 1 − 1 − 1 ] . Concept used: If A = [ a i j ] is an m × n matrix and B = [ b i j ] is an n × k matrix, then their product is the m × k matrix C = [ c i j ] , where c i j is the inner product of the i th row of A and the j th column of B . The product is written as, C = A ⋅ B If the number of columns in A is not equal to number of rows in B , then their product A ⋅ B does not exist. If two matrices A and B are multiplied and the resultant A ⋅ B is an identity matrix I and also the product B ⋅ A is an identity matrix I , then the matrices A and B are inverse of each other. If the number of rows in a matrix is m and the number of columns in a matrix is n , then the dimension of that particular matrix can be written as m × n . Calculation: The dimension of matrix A is 3 × 3 and dimension of matrix B is 3 × 3 , therefore, number of columns in A is equal to number of rows in B and hence the product matrix A ⋅ B with dimension as 3 × 3 exists. The matrix A is multiplied with B as follows. 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 ) ] = [ 1 0 0 0 1 0 0 0 1 ] Therefore, the product A ⋅ B is an identity matrix

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 6, Problem 46E

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To verify:

That the matrices A=[2−132−21011] and B=[− 3 22 5 2−1121−1−1] are inverse of each other.

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Chapter 6, Problem 45E

Chapter 6, Problem 47E

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To verify: That the 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 inverse of each other.

Solution Summary: The author explains that the matrices A and B are inverse of each other.

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To verify:

That the matrices A=[2−132−21011] and B=[− 3 22 5 2−1121−1−1] are inverse of each other.

Want to see the full answer?

Chapter 6 Solutions

To verify: That the 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 inverse of each other.

Solution Summary: The author explains that the matrices A and B are inverse of each other.

Concept explainers

Videos

To verify: That the matrices A=[2−132−21011] and B=[− 3 22 5 2−1121−1−1] are inverse of each other.

Want to see the full answer?

Chapter 6 Solutions

To verify:

That the matrices A=[2−132−21011] and B=[− 3 22 5 2−1121−1−1] are inverse of each other.