## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 8 - Section 8.4 - Multiplicative Inverses of Matrices and Matrix Equations - Exercise Set - Page 932: 17

#### Answer

The matrix does not have an inverse.

#### Work Step by Step

Consider the given matrix $A=\left[ \begin{matrix} 10 & -2 \\ -5 & 1 \\ \end{matrix} \right]$ Now, by using the inverse formula, we get: ${{A}^{-1}}=\frac{1}{\left| ad-bc \right|}\left[ \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right]$ Let, \begin{align} & a=10 \\ & b=-2 \\ & c=-5 \\ & d=1 \end{align} Substitute the values to get, \begin{align} & {{A}^{-1}}=\frac{1}{\left| ad-bc \right|}\left[ \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right] \\ & {{A}^{-1}}=\frac{1}{\left| 10\times 1-\left( -2 \right)\times \left( -5 \right) \right|}\left[ \begin{matrix} 1 & 2 \\ 5 & 10 \\ \end{matrix} \right] \\ & =\frac{1}{10-10}\left[ \begin{matrix} 2 & -3 \\ 1 & 2 \\ \end{matrix} \right] \\ & =\frac{1}{0}\left[ \begin{matrix} 2 & -3 \\ 1 & 2 \\ \end{matrix} \right] \end{align} So, the matrix is not invertible. Therefore, the matrix does not have an inverse because $ab-bc=0$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.