Chapter 8.3, Problem 22E

To determine

Tofind:the inverse of the matrix if it’s exists.

Answer to Problem 22E

Theinverse of matrix A doesn’t exist.

Explanation of Solution

Given:

  $\text{A=}\left[\begin{array}{ccc}\text{1}& \text{0}& \text{0}\\ \text{3}& \text{0}& \text{9}\\ \text{2}& \text{5}& \text{5}\end{array}\right]$

Concept used:

Steps to solve the inverse of matrix by

Step1: calculating the matrix of minors.

Step2:turn that into the matrix of cofactors.

Step3: then ad jugate by transposing the cofactor.

Step4: last multiply by the $\frac{1}{\text{determinant}}$ .

Formula for inverse of matrix A is:

  ${\text{A}}^{\text{-1}}\text{=}\frac{\text{adjA}}{\left|\text{A}\right|}$

Calculation:

Here $\text{A=}\left[\begin{array}{ccc}\text{1}& \text{0}& \text{0}\\ \text{3}& \text{0}& 0\\ \text{2}& \text{5}& \text{5}\end{array}\right]$

  $\left|\text{A}\right|=0+0+0=0.$

  ${\text{A}}^{\text{-1}}\text{=}\frac{\text{adjA}}{\left|\text{A}\right|}$

Since determinant of A is 0 any number divided by 0 doesn’t exist

Hence, inverse of matrix A doesn’t exist.

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