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 934: 71

Answer

The expression is, $ X=\left[ \begin{align} & \,\,\,2 \\ & \,\,\,3 \\ & -5 \\ \end{align} \right]$

Work Step by Step

Consider the given system of equations, $\begin{align} & x-y+z=-6 \\ & 4x+2y+z=9 \\ & 4x-2y+z=-3 \end{align}$ The linear system can be written as, $ AX=B $ $\left[ \begin{matrix} 1 & -1 & 1 \\ 4 & 2 & 1 \\ 4 & -2 & 1 \\ \end{matrix} \right]\left[ \begin{matrix} x \\ y \\ z \\ \end{matrix} \right]=\left[ \begin{matrix} -6 \\ 9 \\ -3 \\ \end{matrix} \right]$ The solution is given by $ X={{A}^{-1}}B $; consequently, we must find ${{A}^{-1}}B $ by using a graphic calculator. We will follow the steps given below: (1) Select the matrix $ A $ from the matrix edit menu and then enter or accept the dimensions. Next, select the matrix $ B $ and enter the elements in the matrix. (2) Use ${{2}^{nd}}$ and press the matrix button. (3) Select the matrix $ A $ and use the enter button and then use the function ${{X}^{-1}}$ for multiplication of the matrix. (4) Then use the ${{2}^{nd}}$ button and press the matrix button or select matrix $ B $ and press the enter button. (5) Press the enter button to get the value of ${{A}^{-1}}B $. Therefore, $ X=\left[ \begin{align} & \,\,\,2 \\ & \,\,\,3 \\ & -5 \\ \end{align} \right]$
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