Precalculus (6th Edition) Blitzer

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

Chapter 8 - Section 8.4 - Multiplicative Inverses of Matrices and Matrix Equations - Exercise Set - Page 932: 36

Answer

The linear system can be written as: $\begin{align} & -x+z=-4 \\ & -y=2 \\ & y+z=4 \end{align}$
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Work Step by Step

Now, compare the coefficients with the provided matrix $\begin{align} & {{a}_{1}}=-1 \\ & {{a}_{2}}=0 \\ & {{a}_{3}}=0 \end{align}$ $\begin{align} & {{b}_{1}}=0 \\ & {{b}_{2}}=-1 \\ & {{b}_{3}}=1 \end{align}$ $\begin{align} & {{c}_{1}}=1 \\ & {{c}_{2}}=0 \\ & {{c}_{3}}=1 \end{align}$ And $\begin{align} & {{d}_{1}}=-4 \\ & {{d}_{2}}=2 \\ & {{d}_{3}}=4 \end{align}$ Substitute the values in the linear equation $\begin{align} & {{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z={{d}_{1}} \\ & {{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z={{d}_{2}} \\ & {{a}_{3}}x+{{b}_{2}}y+{{c}_{3}}z={{d}_{3}} \end{align}$ So, $\begin{align} & -x+z=-4 \\ & -y=2 \\ & y+z=4 \end{align}$
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