Answer
Coefficient Matrix $=\begin{bmatrix} 1 & 2 \\ 2 & 3\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} x \\ y\end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 11 \\ 18\end{bmatrix}$
Our matrix equation is:
$\begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix} \begin{bmatrix} x \\
y\end{bmatrix} =\begin{bmatrix} 11 \\ 18 \end{bmatrix}$
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 $$x + 2y=11 \\ 2x+3y=18$$
Our matrix equation is:
$\begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix} \begin{bmatrix} x \\
y\end{bmatrix} =\begin{bmatrix} 11 \\ 18 \end{bmatrix}$
Our required results are:
Coefficient Matrix $=\begin{bmatrix} 1 & 2 \\ 2 & 3\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} x \\ y\end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 11 \\ 18\end{bmatrix}$
