Answer
Coefficient Matrix $=\begin{bmatrix} 1 &1 \\ 1 & -2\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} x \\
y\end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 5 \\- 4\end{bmatrix}$
Our matrix equation is:
$\begin{bmatrix} 1 &1 \\ 1 & -2\end{bmatrix} \begin{bmatrix} x \\
y\end{bmatrix} =\begin{bmatrix} 5 \\- 4\end{bmatrix}$
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 that $$x +y=5 \\ x-2y=-4$$
Our matrix equation is:
$\begin{bmatrix} 1 &1 \\ 1 & -2\end{bmatrix} \begin{bmatrix} x \\
y\end{bmatrix} =\begin{bmatrix} 5 \\- 4\end{bmatrix}$
Our required results are:
Coefficient Matrix $=\begin{bmatrix} 1 &1 \\ 1 & -2\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} x \\
y\end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 5 \\- 4\end{bmatrix}$
