## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 725: 49

#### Answer

Part A: $\begin{bmatrix} 19\\ 48\\ \end{bmatrix}$ Part B: Not possible. Part C: $\begin{bmatrix} 14 & -8\\ 16 & 142\\ \end{bmatrix}$

#### Work Step by Step

A has 2 rows and 2 columns (2 x 2). B has 2 rows and 1 column (2 x 1). Part A: $\begin{bmatrix} (-4)(-6) + (-1)(5)\\ 2(-6) + 12(5)\\ \end{bmatrix}$ = $\begin{bmatrix} 24 - 5\\ -12 + 60\\ \end{bmatrix}$ = $\begin{bmatrix} 19\\ 48\\ \end{bmatrix}$ Part B: Since the number of columns in B does not equal the number of rows in A, BA is not possible. Part C: $\begin{bmatrix} (-4)(-4) + (-1)(2) & (-4)(-1) + (-1)(12)\\ 2(-4) + 12(2) & 2(-1) + 12(12)\\ \end{bmatrix}$ = $\begin{bmatrix} 16 - 2 & 4 - 12\\ -8 + 24 & -2 + 144\\ \end{bmatrix}$ = $\begin{bmatrix} 14 & -8\\ 16 & 142\\ \end{bmatrix}$

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