## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 725: 35

#### Answer

$AB$ is an $3\times2$ matrix. $AB=\begin{bmatrix} -2 & 51 \\ -8 & 33 \\ 0 & 27 \end{bmatrix}$

#### Work Step by Step

$A$ is an $3\times2$ matrix and $B$ is an $2\times2$ matrix. The number of columns of $A$ is equal to the number of rows of $B$. So, it is possible to find $AB$, where $AB$ is a $3\times2$ matrix. $\begin{bmatrix} -1 & 6 \\ -4 & 5 \\ 0 & 3 \end{bmatrix}·\begin{bmatrix} 2 & 3 \\ 0 & 9 \end{bmatrix}=\begin{bmatrix} -1(2)+6(0) & -1(3)+6(9) \\ -4(2)+5(0) & -4(3)+5(9) \\ 0(2)+3(0) & 0(3)+3(9) \end{bmatrix}=\begin{bmatrix} -2 & 51 \\ -8 & 33 \\ 0 & 27 \end{bmatrix}$

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