Explanation Approach: Let A be a n × n matrix and let I n be n × n identity matrix. Write the n × n matrix that consist of the given matrix A on the left and the n × n identity matrix on the right to obtain. [ A ⋮ I ] The result will be the matrix, [ I ⋮ A − 1 ] If this is not possible, then A is not invertible. Check if A A − 1 = I Calculation: Let us denote the given matrix by A . A = [ 1 1 1 3 5 4 3 6 5 ] Proceed by adjoining the identity matrix to form the matrix, [ A ⋮ I ] = [ 1 1 1 ⋮ 1 0 0 3 5 4 ⋮ 0 1 0 3 6 5 ⋮ 0 0 1 ] Use the elementary row operation to obtain the form of [ I ⋮ A − 1 ] . Apply operation R 3 → R 3 − 3 R 1 and R 2 → R 2 − 3 R 1 [ A ⋮ I ] = [ 1 1 1 ⋮ 1 0 0 0 2 1 ⋮ − 3 1 0 0 3 2 ⋮ − 3 0 1 ] Apply operation R 2 → 1 2 R 2 . [ A ⋮ I ] = [ 1 1 1 ⋮ 1 0 0 0 1 1 / 2 ⋮ − 3 / 2 1 / 2 0 0 3 2 ⋮ − 3 0 1 ] Apply operation R 1 → R 1 − R 2 and R 3 → R 3 − 3 R 2 . [ A ⋮ I ] = [ 1 0 1 / 2 ⋮ 5 / 2 − 1 / 2 0 0 1 1 / 2 ⋮ − 3 / 2 1 / 2 0 0 0 1 / 2 ⋮ 3 / 2 − 3 / 2 1 ] Apply operation R 3 → 1 2 R 3 . [ A ⋮ I ] = [ 1 0 1 / 2 ⋮ 5 / 2 − 1 / 2 0 0 1 1 / 2 ⋮ − 3 / 2 1 / 2 0 0 0 1 ⋮ 3 − 3 2 ] Apply operation R 1 → R 1 − 1 2 R 3 and R 2 → R 2 − 1 2 R 3

Bundle: Precalculus, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Precalculus, 10th Edition, Single-Term

10th Edition

ISBN: 9781337605090

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 8.3, Problem 19E

To determine

To find:

The inverse of matrix [111354365].

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Chapter 8.3, Problem 18E

Chapter 8.3, Problem 20E

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Chapter 8 Solutions

Bundle: Precalculus, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Precalculus, 10th Edition, Single-Term

Ch. 8.1 - Prob. 1CP Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 5CP Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 8.1 - Prob. 8CP Ch. 8.1 - Prob. 9CP Ch. 8.1 - Prob. 1E

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