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

4th Edition

ISBN: 8220100548512

Author: Watson

Publisher: CENGAGE L

See similar textbooks

Videos

Question

Chapter 11.CR, Problem 59E

To determine

To find:

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.CR, Problem 58E

Chapter 11.CR, Problem 60E

Students have asked these similar questions

Solve for the matrix X: X (2 7³) x + ( 2 ) - (112) 6 14 8

5. Solve for the matrix X. (Hint: we can solve AX -1 = B whenever A is invertible) 2 3 0 Χ 2 = 3 1

Write p(x) = 6+11x+6x² as a linear combination of ƒ (x) = 2+x+4x² and g(x) = 1−x+3x² and h(x)=3+2x+5x²

Chapter 11 Solutions

EBK ALGEBRA AND TRIGONOMETRY

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

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

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.