College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 6 - Matrices and Determinants - Exercise Set 6.2 - Page 609: 25


a. $\left\{\begin{array}{l} 4w-2x+2y-3z=0\\ 7w-x-y-3z=0\\ w+x-y-z=0 \end{array}\right.$ b. $\{(0.5z,\ 0,\ 0.5z$, $z), z \in R\}$.

Work Step by Step

a. The augmented matrix has 5 columns, so there are 4 variables. Let the variables be w,x,y, and z. System of equations: $\left\{\begin{array}{l} 4w-2x+2y-3z=0\\ 7w-x-y-3z=0\\ w+x-y-z=0 \end{array}\right.$ b. The reduced system: $\left\{\begin{array}{l} w-0.5z=0\\ x=0\\ y-0.5z=0 \end{array}\right.$ Taking z as a parameter, express $w$ and $y$ in terms of $z$. $w-0.5z=0 \Rightarrow w=0.5z$ $y-0.5z=0 \Rightarrow y=0.5z$ The solution set is $\{(0.5z,\ 0,\ 0.5z$, $z), z \in R\}$.
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