Explanation Approach: Let A be a n × n matrix and let I n be n × n identity matrix. If there exist a matrix A − 1 such that A A − 1 = I n And, A − 1 A = I n Then A − 1 is the inverse of A. Calculation: B is the inverse of A only if, A B = I ... ( 1 ) And, B A = I ... ( 2 ) Substitute [ − 1 − 1 − 3 − 2 ] for B , [ 1 0 0 1 ] for I and [ 2 − 1 − 3 1 ] for A in equation ( 1 ) . [ 2 − 1 − 3 1 ] [ − 1 − 1 − 3 − 2 ] = [ 1 0 0 1 ] [ ( 2 ) ( − 1 ) + ( − 1 ) ( − 3 ) ( 2 ) ( − 1 ) + ( − 1 ) ( − 2 ) ( − 3 ) ( − 1 ) + ( 1 ) ( − 3 ) ( − 3 ) ( − 1 ) + ( 1 ) ( − 2 ) ] = [

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Chapter 8.3, Problem 1CP

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The matrix B=[−1−1−3−2] is the inverse of matrix A=[2−1−31].

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Chapter 8.2, Problem 92E

Chapter 8.3, Problem 2CP

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The matrix B = [ − 1 − 1 − 3 − 2 ] is the inverse of matrix A = [ 2 − 1 − 3 1 ] .

Solution Summary: The author explains that the matrix B=left[cc-1& -1 -3& 1end

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To show:

The matrix B=[−1−1−3−2] is the inverse of matrix A=[2−1−31].

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Chapter 8 Solutions

The matrix B = [ − 1 − 1 − 3 − 2 ] is the inverse of matrix A = [ 2 − 1 − 3 1 ] .

Solution Summary: The author explains that the matrix B=left[cc-1& -1 -3& 1end

Concept explainers

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To show: The matrix B=[−1−1−3−2] is the inverse of matrix A=[2−1−31].

Want to see the full answer?

Chapter 8 Solutions

To show:

The matrix B=[−1−1−3−2] is the inverse of matrix A=[2−1−31].