   Chapter 11.CT, Problem 18CT ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# TESTOnly one of the following matrix has an inverse. Find the determinant of each matrix, and use the determinant to identify the one that has an inverse. Then find the inverse. A = [ 1 4 1 0 2 0 1 0 1 ] B = [ 1 4 0 0 2 0 − 3 0 1 ]

To determine

To find:

The determinant of the given matrices and identify which one has an inverse.

Explanation

Given:

Two matrices are

A=

B=

Approach:

The determinant of matrix A=[abcdefghi] is given by

|abcdefghi|=a|efhi|b|dfgi|+c|degh|.

A given matrix has an inverse if and only if its determinant is non-zero.

Calculation:

Consider the matrix A=

Then, |A| is

|141020100|=1|2001|4|0010|+1|0210|=(20)4(00)+(02)=22=0

Now, |B| is

|140020301|=1|2001|4|0031|+0|0230|=1(20)4(00)+0(0+6)=20+0=2

Since |A|=0 therefore, it doesn’t have an inverse

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