Answer
Coefficient Matrix $=\begin{bmatrix} 1 & 3 &-1 \\ 1 & 0 & 2 \\ 0 &2 &-1\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} x \\ y \\ z \end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 2 \\ 8 \\ 1 \end{bmatrix}$
Our matrix equation is:
$\begin{bmatrix} 1 & 3 &-1 \\ 1 & 0 & 2 \\ 0 &2 &-1\end{bmatrix} \begin{bmatrix} x \\ y \\ z\end{bmatrix} =\begin{bmatrix} 2 \\ 8 \\1 \end{bmatrix}$
Work Step by Step
Write the given system of equations into the matrix form in order to label the parts of the matrix equation.
Re-arrange the given system of equations as follows: $$x+3y-z=2 \\ x+(0) y+2z=8 \\ 0 x+2y-z=1$$
Our matrix equation is:
$\begin{bmatrix} 1 & 3 &-1 \\ 1 & 0 & 2 \\ 0 &2 &-1\end{bmatrix} \begin{bmatrix} x \\ y \\ z\end{bmatrix} =\begin{bmatrix} 2 \\ 8 \\1 \end{bmatrix}$
Our required results are:
Coefficient Matrix $=\begin{bmatrix} 1 & 3 &-1 \\ 1 & 0 & 2 \\ 0 &2 &-1\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} x \\ y \\ z \end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 2 \\ 8 \\ 1 \end{bmatrix}$
