Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 10 - 10.4 - The Determinant of a Square Matrix - 10.4 Exercises - Page 744: 102a


There is a row of all zeroes.

Work Step by Step

The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$ where $det =\begin{bmatrix}p & q \\r & s\end{bmatrix}$ we have $\begin{bmatrix}2 & -4 & 5 \\1 & -2&3 \\0 & 0& 0\end{bmatrix}$ It can be seen that there is a row of all zeroes. When one row of a matrix is all zeros, then each factor is multiplied by $0$. Thus, the determinant is zero.
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