Answer
The linear system can be written as:
$\begin{align}
& {{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z={{d}_{1}} \\
& {{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z={{d}_{2}} \\
& {{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}z={{d}_{3}}
\end{align}$
Work Step by Step
A linear equation of the multiplication matrix is given by,
$\begin{align}
& {{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z={{d}_{1}} \\
& {{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z={{d}_{2}} \\
& {{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}z={{d}_{3}}
\end{align}$
Thus, a linear system of three-variables of linear equations is
$\begin{align}
& {{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z={{d}_{1}} \\
& {{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z={{d}_{2}} \\
& {{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}z={{d}_{3}}
\end{align}$
