Explanation Strategy for finding the inverse of a matrix: If a sequence of a row operations performed on the n × n matrix A reduces A to the n × n identity matrix I , then those same row operations, performed in the same order on I , will transform I into A − 1 . If no sequence of row operations will reduce A to I , then A is not invertible. A notation for this process uses an n -row-by- 2 n -column matrix, with matrix A as the left half and matrix I as the right half. If A is invertible, the proper row operations on [ A | I ] will transfer it into [ I | A − 1 ] . Given: The given matrix is, [ 1 2 3 0 1 1 0 − 1 0 ] Calculation: Let A = [ 1 2 3 0 1 1 0 − 1 0 ] We can set up a 3 × 6 matrix with A on the left and I on the right of the line, [ A | I ] = [ 1 2 3 0 1 1 0 − 1 0 | 1 0 0 0 1 0 0 0 1 ] We perform row operations on the entire matrix to transform the left half into I . [ A | I ] = [ 1 2 3 0 1 1 0 − 1 0 | 1 0 0 0 1 0 0 0 1 ] R 3 → R 3 + R 2 [ 1 2 3 0 1 1 0 0 1 | 1 0 0 0 1 0 0 1 1 ] R 2 → R 2 − R 3 [ 1 2 3 0 1 0 0 0 1 | 1 0 0 0 0 − 1 0 1 1 ] Ȁ

12th Edition

ISBN: 9781305652231

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

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Chapter 6.4, Problem 16E

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The inverse of matrix [1230110−10] if possible.

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Chapter 6.4, Problem 15E

Chapter 6.4, Problem 17E

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The inverse of matrix [ 1 2 3 0 1 1 0 − 1 0 ] if possible.

Solution Summary: The author explains how to find the inverse of matrix A-1. If a sequence of row operations reduces A to I, they transform it into

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To find:

The inverse of matrix [1230110−10] if possible.

Want to see the full answer?

Chapter 6 Solutions

The inverse of matrix [ 1 2 3 0 1 1 0 − 1 0 ] if possible.

Solution Summary: The author explains how to find the inverse of matrix A-1. If a sequence of row operations reduces A to I, they transform it into

Videos

To find: The inverse of matrix [1230110−10] if possible.

Want to see the full answer?

Chapter 6 Solutions

To find:

The inverse of matrix [1230110−10] if possible.