Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 10 - Systems of Equations and Inequalities - Section 10.4 Matrix Algebra - 10.4 Assess Your Understanding - Page 777: 13

Answer

$\begin{bmatrix} -8 & 7 & -15\\ 7 & 0 & 22 \end{bmatrix}$

Work Step by Step

Since, matrices $A$ and $B$ are both $ 2 \times 3$ matrices and have the same dimensions, we know that their subtraction, $3A-2B$, is defined. $3A-2B=3 \begin{bmatrix} 0 & 3 & -5\\ 1 & 2 & 6 \end{bmatrix}-2\begin{bmatrix} 4 & 1 & 0\\ -2 & 3 & -2 \end{bmatrix} \\=\begin{bmatrix} 3\cdot 0 & 3\cdot 3 & 3\cdot(-5)\\ 3\cdot 1 & 3\cdot 2 & 3\cdot 6 \end{bmatrix}-\begin{bmatrix} 2\cdot 4 & 2\cdot 1 & 2\cdot 0\\ 2\cdot(-2) & 2\cdot 3 & 2\cdot(-2) \end{bmatrix} \\=\begin{bmatrix} 0-8 & 9-2 & -15-0\\ 3-(-4) & 6-6 & 18-(-4) \end{bmatrix}\\=\begin{bmatrix} -8 & 7 & -15\\ 7 & 0 & 22 \end{bmatrix}$
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