Explanation Approach: Take a 4 × 8 matrix with left half as matrix B and right half as I 4 and transform the left half into identity matrix by performing elementary row operations on the entire matrix, the right half becomes inverse of the matrix B . Calculation: Consider the determinant A = | 1 0 0 1 0 2 0 2 0 0 3 3 0 0 0 4 | . Expand the determinant by fourth row. det ( A 44 ) = | 1 0 0 0 2 0 0 0 3 | = 1 ( − 1 ) 1 + 1 | 2 0 0 3 | = 1 ( 2 ⋅ 3 − 0 ⋅ 0 ) = 6 det ( A ) = 0 ( − 1 ) 4 + 1 A 41 + 0 ( − 1 ) 4 + 2 A 42 + 0 ( − 1 ) 4 + 3 A 43 + 4 ( − 1 ) 4 + 4 6 = 0 + 0 + 0 + 24 = 24 Since, det ( A ) ≠ 0 , the inverse of the matrix exists. Inverse of the matrix is shown below: Consider a matrix, [ 1 0 0 1 0 2 0 2 0 0 3 3 0 0 0 4 | 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] Perform the transformation R 2 → 1 2 R 2 . [ 1 0 0 1 0 ( 1 2 ) 2 ( 1 2 ) 0 ( 1 2 ) 2 ( 1 2 ) 0 0 3 3 0 0 0 4 | 1 0 0 0 0 ( 1 2 ) 1 ( 1 2 ) 0 ( 1 2 ) 0 ( 1 2 ) 0 0 1 0 0 0 0 1 ] → [ 1 0 0 1 0 1 0 1 0 0 3 3 0 0 0 4 | 1 0 0 0 0 1 2 0 0 0 0 1 0 0 0 0 1 ] Perform the transformation R 3 → 1 3 R 3 . [ 1 0 0 1 0 1 0 1 0 ( 1 3 ) 0 ( 1 3 ) 3 ( 1 3 ) 3 ( 1 3 ) 0 0 0 4 | 1 0 0 0 0 1 2 0 0 0 ( 1 3 ) 0 ( 1 3 ) 1 ( 1 3 ) 0 ( 1 3 ) 0 0 0 1 ] → [ 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 4 | 1 0 0 0 0 1 2 0 0 0 0 1 3 0 0 0 0 1 ] Perform the transformation R 4 → 1 4 R 4 . [ 1 0 0 1 0 1 0 1 0 0 1 1 0 ( 1 4 ) 0 ( 1 4 ) 0 ( 1 4 ) 4 ( 1 4 ) | 1 0 0 0 0 1 2 0 0 0 0 1 3 0 0 ( 1 4 ) 0 ( 1 4 ) 0 ( 1 4 ) 1 ( 1 4 ) ] → [ 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 | 1 0 0 0 0 1 2 0 0 0 0 1 3 0 0 0 0 1 4 ] Perform the transformation R 1 → R 1 − R 4

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 11.CR, Problem 59E

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The determinant of the matrix [1001020200330004], and the inverse, if it exists.

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Chapter 11.CR, Problem 58E

Chapter 11.CR, Problem 60E

Chapter 11 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 11.1 - If a system of linear equations has infinitely...Ch. 11.1 - Write the augmented matrix of the following system...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - 5-10 Dimension of a Matrix State the dimension of...Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The determinant of the matrix [ 1 0 0 1 0 2 0 2 0 0 3 3 0 0 0 4 ] , and the inverse, if it exists.

Solution Summary: The author analyzes the determinant of a 4times 8 matrix with left half as matrix B, and inverse by performing elementary row operations on the entire matrix.

Videos

To find:

The determinant of the matrix [1001020200330004], and the inverse, if it exists.

Want to see the full answer?

Chapter 11 Solutions

The determinant of the matrix [ 1 0 0 1 0 2 0 2 0 0 3 3 0 0 0 4 ] , and the inverse, if it exists.

Solution Summary: The author analyzes the determinant of a 4times 8 matrix with left half as matrix B, and inverse by performing elementary row operations on the entire matrix.

Videos

To find: The determinant of the matrix [1001020200330004], and the inverse, if it exists.

Want to see the full answer?

Chapter 11 Solutions

To find:

The determinant of the matrix [1001020200330004], and the inverse, if it exists.