Answer
See answers below
Work Step by Step
$\begin{bmatrix}
2 & -2 & 1 & 3\\
3 & -2 & 3 & 1\\
1 & -1 & 1 &0\\
2 & -1 & 2 &2
\end{bmatrix} \approx^1 \begin{bmatrix}
1 & -1 & 1 & 0\\
3 & -2 & 3 & 1\\
2& -2 & -1 &3\\
2 & -1 & 2 &2
\end{bmatrix} \approx^2 \begin{bmatrix}
1 & -1 & 1 & 0\\
0 & 1 & 0 & 1\\
0& 0 & -3 &3\\
0 & 1 & 0 &2
\end{bmatrix} \approx^3 \begin{bmatrix}
1 & -1 & 1 & 0\\
0 & 1 & 0 & 1\\
0& 0 & -3 &3\\
0 & 0 & 0 &1
\end{bmatrix} \approx^4 \begin{bmatrix}
1 & -1 & 1 & 0\\
0 & 1 & 0 & 1\\
0& 0 & 1&-1\\
0 & 0 & 0 &1
\end{bmatrix} $
Rank (A)= 4
$P_{13}$
$A_{12}(-3), A_{13}(-2), A_{14}(-2)$
$A_{24}(-1)$
$M_3(\frac{1}{3})$
