Answer
The statement is False and the correct solution is
$\left[ \begin{array}{*{35}{l}}
1 & -3 & 0 & 5 \\
0 & 1 & -2 & 7 \\
2 & 0 & 1 & 4 \\
\end{array} \right]$.
Work Step by Step
Consider the system of given equations
$\begin{align}
& {{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z={{d}_{1}} \\
& {{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z={{d}_{2}} \\
& {{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}z={{d}_{3}}
\end{align}$
The augmented matrix for above equations can be written as below:
$\left[ \begin{array}{*{35}{l}}
{{a}_{1}} & {{b}_{1}} & {{c}_{1}} & {{d}_{1}} \\
{{a}_{2}} & {{b}_{2}} & {{c}_{2}} & {{d}_{2}} \\
{{a}_{3}} & {{b}_{3}} & {{c}_{3}} & {{d}_{3}} \\
\end{array} \right]$
Therefore, the provided system of equations is:
$\begin{align}
& x-3y=5 \\
& y-2z=7 \\
& 2x+z=4
\end{align}$
The augmented matrix is given by:
$\left[ \begin{array}{*{35}{l}}
1 & -3 & 0 & 5 \\
0 & 1 & -2 & 7 \\
2 & 0 & 1 & 4 \\
\end{array} \right]$
Hence, the provided statement is false and the correct solution is
$\left[ \begin{array}{*{35}{l}}
1 & -3 & 0 & 5 \\
0 & 1 & -2 & 7 \\
2 & 0 & 1 & 4 \\
\end{array} \right]$.
