To create a matrix of an equation system, we take the coefficients of each equation and create the matrix A:
[tex]\begin{gathered} 5x-3y+4z=-12 \\ 3x+2y+2z=-5 \\ x-y+2z=2 \end{gathered}[/tex][tex]A=\begin{bmatrix}{5} & {-3} & {4} \\ {3} & {2} & {2} \\ {1} & {-1} & {2}\end{bmatrix}[/tex]
And take the right hand side of the equation and create the column matrix B:
[tex]B=\begin{bmatrix}{-12} & {} & {} \\ {-5} & {} & {} \\ {2} & {} & {}\end{bmatrix}[/tex]
Then, the system of equations in matrix multiplication is:
[tex]AX=B\Rightarrow\begin{bmatrix}{5} & {-3} & {4} \\ {3} & {2} & {2} \\ {1} & {-1} & {2}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {z} & {} & {}\end{bmatrix}=\begin{bmatrix}{-12} & {} & {} \\ {-5} & {} & {} \\ {2} & {} & {}\end{bmatrix}[/tex]
