Answer
See below.
Work Step by Step
We know that
\[
\left\{
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3=d_3 \\
\end{array}
\right.
\]
becomes
\[
\left[\begin{array}{rrr|r}
a_1 & b_1 & c_1 & d_1 \\
a_2 & b_2 & c_2 & d_2 \\
a_3 & b_3 & c_3 & d_3 \\
\end{array} \right]
\]
Thus the statement is false, the correct augmented matrix is: \[
\left[\begin{array}{rrr|r}
1 & -3 & 0 & 5 \\
0 & 1 & -2 & 7 \\
2 & 0 & 1 & 4 \\
\end{array} \right]
\]
