Answer
See answers below
Work Step by Step
$\begin{bmatrix}
0 & 1 & 2 &1\\
0& 3 & 1 & 2\\
0 & 0 & 0& 1
\end{bmatrix} \approx^1\begin{bmatrix}
0 & 1 & 2 &1\\
0& 0 & -6 & -2\\
0 & 0 & -4& -1
\end{bmatrix} \approx^2 \begin{bmatrix}
0 & 1 & 2 &1\\
0& 0 & 1 &\frac{1}{3}\\
0 & 0 & -4& -1
\end{bmatrix} \approx^3\begin{bmatrix}
0 & 1 & 0 &\frac{1}{3}\\
0& 0 & 1 &\frac{1}{3}\\
0 & 0 & 0& \frac{1}{3}
\end{bmatrix} \approx^4\begin{bmatrix}
0 & 1 & 0 &\frac{1}{3}\\
0& 0 & 1 &\frac{1}{3}\\
0 & 0 & 0& 1
\end{bmatrix} \approx^5\begin{bmatrix}
0 & 1 & 0 &0\\
0& 0 & 1 &0\\
0 & 0 & 0& 1
\end{bmatrix}$
Rank (A)= 3
The last matrix is in a row-echelon form.
$A_{12}(-3),A_{13}(-2)$
$M_2(-\frac{1}{6})$
$A_{21}(-2),A_{23}(4)$
$M_3(3)$
$A_{32}(-\frac{1}{3}),A_{31}(-\frac{1}{3})$
