Answer
For the linear system
$\left\{\begin{array}{l}
a_{1}x+b_{1}y+c_{1}z=d_{1}\\
a_{2}x+b_{2}y+c_{2}z=d_{2}\\
a_{3}x+b_{3}y+c_{3}z=d_{3 }
\end{array}\right.$
the matrix form of the system is
$AX=B$
$\left[\begin{array}{lll}
a_{1} & b_{1} & c_{1}\\
a_{2} & b_{2} & c_{2}\\
a_{3} & b_{3} & c_{3}
\end{array}\right]\left[\begin{array}{l}
x\\
y\\
z
\end{array}\right]=\left[\begin{array}{l}
d_{1}\\
d_{2}\\
d_{3}
\end{array}\right]$
Work Step by Step
For the linear system
$\left\{\begin{array}{l}
a_{1}x+b_{1}y+c_{1}z=d_{1}\\
a_{2}x+b_{2}y+c_{2}z=d_{2}\\
a_{3}x+b_{3}y+c_{3}z=d_{3 }
\end{array}\right.$
We define the coefficient matrix, $A=\left[\begin{array}{lll}
a_{1} & b_{1} & c_{1}\\
a_{2} & b_{2} & c_{2}\\
a_{3} & b_{3} & c_{3}
\end{array}\right]$
and two column matrices,
$X=\left[\begin{array}{l}
x\\
y\\
z
\end{array}\right],\ B=\left[\begin{array}{l}
d_{1}\\
d_{2}\\
d_{3}
\end{array}\right].$
The matrix form of the system is
$AX=B$
$\left[\begin{array}{lll}
a_{1} & b_{1} & c_{1}\\
a_{2} & b_{2} & c_{2}\\
a_{3} & b_{3} & c_{3}
\end{array}\right]\left[\begin{array}{l}
x\\
y\\
z
\end{array}\right]=\left[\begin{array}{l}
d_{1}\\
d_{2}\\
d_{3}
\end{array}\right]$
