Explanation Given information: The given equations are x + 2 y − z = − 2 , 3 x + 5 y − z = − 5 , and − 2 x − y − 2 z = − 5 . Calculation: Use the given Equations and form matrix A . Express matrix A as follows: A = [ 1 2 − 1 3 5 − 1 − 2 − 1 − 2 ] Express the matrix C as follows: C = [ − 2 − 5 − 5 ] Determine the adj A of matrix A using the relation. adj A = [ [ 5 − 1 − 1 − 2 ] [ 3 − 1 − 2 − 2 ] [ 3 5 − 2 − 1 ] [ 2 − 1 − 1 − 2 ] [ 1 − 1 − 2 − 2 ] [ 1 2 − 2 − 1 ] [ 2 − 1 5 − 1 ] [ 1 − 1 3 − 1 ] [ 1 2 3 5 ] ] = [ ( 5 × − 2 − ( − 1 × − 1 ) ) ( 3 × − 2 − ( − 2 × − 1 ) ) ( 3 × − 1 − ( − 2 × 5 ) ) ( 2 × − 2 − ( − 1 × − 1 ) ) ( 1 × − 2 − ( − 2 × − 1 ) ) ( 1 × − 1 − ( − 2 × 2 ) ) ( 2 × − 1 − ( 5 × − 1 ) ) ( 1 × − 1 − ( 3 × − 1 ) ) ( 1 × 5 − ( 3 × 2 ) ) ] = [ − 11 − 8 7 − 5 − 4 3 3 2 − 1 ] = [ ( − 1 ) 0 + 0 ( − 11 ) ( − 1 ) 0 + 1 ( − 8 ) ( − 1 ) 0 + 2 ( 7 ) ( − 1 ) 1 + 0 ( − 5 ) ( − 1 ) 1 + 1 ( − 4 ) ( − 1 ) 1 + 2 ( 3 ) ( − 1 ) 2 + 0 ( 3 ) ( − 1 ) 2 + 1 ( 2 ) ( − 1 ) 2 + 2 ( − 1 ) ] adj A = [ − 11 8 7 5 − 4 − 3 3 − 2 − 1 ] [ − 11 8 7 5 − 4 − 3 3 − 2 − 1 ] T = [ − 11 5 3 8 − 4 − 2 7 − 3 − 1 ] Calculate the determinant value of matrix A

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 16.4, Problem 2E

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Chapter 16 Solutions

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Ch. 16.1 - For matrices A and B, find A + B. Ch. 16.1 - Prob. 2PE Ch. 16.1 - Prob. 3PE Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E

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Chapter 16 Solutions