Answer
Coefficient Matrix $=\begin{bmatrix} 1 & -1 & 1 \\ 2 & 0 & 1 \\ 0 & 1 & 3 \end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} r \\ s \\ t \end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 150 \\ 425 \\ 0 \end{bmatrix}$
Our matrix equation is:
$\begin{bmatrix} 1 & -1 & 1 \\ 2 & 0 & 1 \\ 0 & 1 & 3 \end{bmatrix} \begin{bmatrix} r \\ s \\ t \end{bmatrix} =\begin{bmatrix} 150 \\ 425 \\ 0 \end{bmatrix}$
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: $$r-s+t=150\\ 2r+(0) s+t=425 \\ (0)r+s+3t=0$$
Our matrix equation is:
$\begin{bmatrix} 1 & -1 & 1 \\ 2 & 0 & 1 \\ 0 & 1 & 3 \end{bmatrix} \begin{bmatrix} r \\ s \\ t \end{bmatrix} =\begin{bmatrix} 150 \\ 425 \\ 0 \end{bmatrix}$
Our required results are:
Coefficient Matrix $=\begin{bmatrix} 1 & -1 & 1 \\ 2 & 0 & 1 \\ 0 & 1 & 3 \end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} r \\ s \\ t \end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 150 \\ 425 \\ 0 \end{bmatrix}$
