Answer
The linear system can be written as $\left[ \begin{matrix}
1 & 4 & -1 \\
1 & 3 & -2 \\
2 & 7 & -5 \\
\end{matrix} \right]\left[ \begin{matrix}
x \\
y \\
z \\
\end{matrix} \right]=\left[ \begin{matrix}
3 \\
5 \\
12 \\
\end{matrix} \right]$
Work Step by Step
Consider the given system of equations:
$\begin{align}
& x+4y-z=3 \\
& x+3y-2z=5 \\
& 2x+7y-5z=12
\end{align}$
The linear system can be written as: $ AX=B $
$\left[ \begin{matrix}
1 & 4 & -1 \\
1 & 3 & -2 \\
2 & 7 & -5 \\
\end{matrix} \right]\left[ \begin{matrix}
x \\
y \\
z \\
\end{matrix} \right]=\left[ \begin{matrix}
3 \\
5 \\
12 \\
\end{matrix} \right]$
Where, $ A=\left[ \begin{matrix}
1 & 4 & -1 \\
1 & 3 & -2 \\
2 & 7 & -5 \\
\end{matrix} \right]$ $ X=\left[ \begin{align}
& x \\
& y \\
& z \\
\end{align} \right]$ $ B=\left[ \begin{align}
& 3 \\
& 5 \\
& 12 \\
\end{align} \right]$
