Answer
Vector equation:
$$
x_1
\begin{bmatrix}
8\\5\\1
\end{bmatrix}
+
x_2
\begin{bmatrix}
-1\\4\\-3
\end{bmatrix}
=
\begin{bmatrix}
4\\1\\2
\end{bmatrix}
$$
Matrix equation:
$$
\begin{bmatrix}
8&-1\\
5&4\\
1&-3
\end{bmatrix}
\begin{bmatrix}
x_1\\x_2
\end{bmatrix}
=
\begin{bmatrix}
4\\1\\2
\end{bmatrix}
$$
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 third entries correspond to the third 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.
