Answer
Vector equation:
$$
x_1
\begin{bmatrix}
3\\0
\end{bmatrix}
+
x_2
\begin{bmatrix}
1\\1
\end{bmatrix}
+
x_3
\begin{bmatrix}
-5\\4
\end{bmatrix}
=
\begin{bmatrix}
9\\0
\end{bmatrix}
$$
Matrix equation:
$$
\begin{bmatrix}
3&1&-5\\
0&1&4
\end{bmatrix}
\begin{bmatrix}
x_1\\x_2\\x_3
\end{bmatrix}
=
\begin{bmatrix}
9\\0
\end{bmatrix}
$$
Work Step by Step
We convert the system of equations into a vector equation with the same variables above. The first entries of the vectors corresponds to the coefficients of the variables in the first equation; the second entries correspond to the second equation.
The matrix equation is formed by putting all the vectors as the column of a matrix and multiplying them by a vector holding the coefficients in the vector equation.
