Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 2 - Matrices - 2.1 Operations with Matrices - 2.1 Exercises: 3

Answer

$x=2$ $y=3$

Work Step by Step

$\begin{pmatrix} 16 & 4 & 5 & 4\\ -3 & 13 & 15 & 6\\ 0 & 2 & 4 & 0 \end{pmatrix}=\begin{pmatrix} 16 & 4 & 2x+1 & 4\\ -3 & 13 & 15 & 3x\\ 0 & 2 & 3y-5 & 0 \end{pmatrix}$ All we need to do here is compare elements: $5=2x+1$ $6=3x$ $4=3y-5$ The first two equations yield the same result: $5-1=4=2x$ $\quad \quad \quad \quad x=\frac{6}{3}=2$ $\implies x=\frac{4}{2}=2$ $4+5=9=3y$ $y=\frac{9}{3}=3$
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