Answer
Coefficient Matrix $=\begin{bmatrix} 3 & 5 \\ 1 & 1\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} a \\ b \end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 0 \\ 2\end{bmatrix}$
Our matrix equation is:
$\begin{bmatrix} 3 & 5 \\ 1 & 1 \end{bmatrix} \begin{bmatrix} x \\
y\end{bmatrix} =\begin{bmatrix} 0 \\ 2 \end{bmatrix}$
Work Step by Step
Write the given system of equations into the matrix form in order to label the parts of the matrix equation.
We are given the system of equations as follows: $$3a+5b=0 \\ a+b=2$$
Our matrix equation is:
$\begin{bmatrix} 3 & 5 \\ 1 & 1 \end{bmatrix} \begin{bmatrix} x \\
y\end{bmatrix} =\begin{bmatrix} 0 \\ 2 \end{bmatrix}$
Our required results are:
Coefficient Matrix $=\begin{bmatrix} 3 & 5 \\ 1 & 1\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} a \\ b \end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 0 \\ 2\end{bmatrix}$
