Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 8 - Section 8.3 - Matrix Operations and Their Applications - Exercise Set - Page 917: 12

Answer

a. $ \begin{bmatrix} 5 & -2 & 7 \\ -4 & 3 & 1 \end{bmatrix}$ b. $ \begin{bmatrix} 1 & 4 & -5 \\ 2 & 1 & 9 \end{bmatrix}$ c. $ \begin{bmatrix} -12 & -4 & -4 \\ 4 & -8 & -20 \end{bmatrix}$ d. $\begin{bmatrix} 13 & -3 & 15 \\ -9 & 8 & 7 \end{bmatrix}$

Work Step by Step

We are given the matrices: $A=\begin{bmatrix} 3 & 1 & 1 \\ -1 & 2 & 5 \end{bmatrix}$ and $B=\begin{bmatrix} 2 & -3 & 6 \\ -3 & 1 & -4 \end{bmatrix}$ We calculate the sums, differences, and multiplication as follows: a. $A+B=\begin{bmatrix} 3 & 1 & 1 \\ -1 & 2 & 5 \end{bmatrix}+\begin{bmatrix} 2 & -3 & 6 \\ -3 & 1 & -4 \end{bmatrix}=\begin{bmatrix} 5 & -2 & 7 \\ -4 & 3 & 1 \end{bmatrix}$ b. $A-B=\begin{bmatrix} 3 & 1 & 1 \\ -1 & 2 & 5 \end{bmatrix}-\begin{bmatrix} 2 & -3 & 6 \\ -3 & 1 & -4 \end{bmatrix}=\begin{bmatrix} 1 & 4 & -5 \\ 2 & 1 & 9 \end{bmatrix}$ c. $-4A=\begin{bmatrix} -12 & -4 & -4 \\ 4 & -8 & -20 \end{bmatrix}$ d. $3A+2B=\begin{bmatrix} 9 & 3 & 3 \\ -3 & 6 & 15 \end{bmatrix}+\begin{bmatrix} 4 & -6 & 12 \\ -6 & 2 & -8 \end{bmatrix}=\begin{bmatrix} 13 & -3 & 15 \\ -9 & 8 & 7 \end{bmatrix}$
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