Answer
See answers below
Work Step by Step
$\begin{bmatrix}
2 & -1 \\
3 & 2 \\
2 &5
\end{bmatrix} \approx^1 \begin{bmatrix}
3 & 2 \\
2 & -1\\
2 &5
\end{bmatrix} \approx^2 \begin{bmatrix}
1 & 3 \\
2 & -1 \\
2 &5
\end{bmatrix} \approx^3\begin{bmatrix}
1 & 3 \\
0 & -7 \\
0 &-1
\end{bmatrix} \approx^4\begin{bmatrix}
1 & 3 \\
0& -1 \\
0 &-7
\end{bmatrix} \approx^5\begin{bmatrix}
1 & 3 \\
0 & 1 \\
0 &0
\end{bmatrix} $
Rank (A) =2
The rank of each matrix:
$P_{12}$
$A_{21}(-1)$
$A_{12}(-2),A_{13}(-2)$
$P_{23}$
$M_{2}(-1),A_{23}(7)$
