## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 10 - 10.4 - The Determinant of a Square Matrix - 10.4 Exercises - Page 743: 77

#### Answer

Both sides are the same.

#### Work Step by Step

The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$ where $det =\begin{bmatrix}p & q \\r & s\end{bmatrix}$ Considering the left side, we have: $det=wz-xy$ Now, considering the right side we have $det=w(z+cy)-y(x+cw)=wz+wcy-yx-ycw=wz-xy$

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