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]$
