Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 9 - Systems and Matrices - 9.2 Matrix Solution of Linear Systems - 9.2 Exercises: 21

Answer

$\{(2,3)\}$

Work Step by Step

Start with the augmented matrix and attempt to reduce it to diagonal form, with 1s along the diagonal. $\left[\begin{array}{llll} 1 & 1 & | & 5\\ 1 & -1 & | & -1 \end{array}\right]\left\{\begin{array}{l} .\\ \leftarrow(R_{2}-R_{1}). \end{array}\right.$ $\left[\begin{array}{llll} 1 & 1 & | & 5\\ 0 & -2 & | & -6 \end{array}\right]\left\{\begin{array}{l} .\\ \leftarrow(-R_{2}/2). \end{array}\right.$ $\left[\begin{array}{llll} 1 & 1 & | & 5\\ 0 & 1 & | & 3 \end{array}\right]\left\{\begin{array}{l} \leftarrow(R_{1}-R_{2}).\\ . \end{array}\right.$ $\left[\begin{array}{llll} 1 & 0 & | & 2\\ 0 & 1 & | & 3 \end{array}\right]$ $x=2$ $y=3$ Solution set: $\{(2,3)\}$
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