Answer
See answers below
Work Step by Step
$\begin{bmatrix}
2 & 1 &4\\
2 & -3 & 4 \\
3 &-2 &6
\end{bmatrix} \approx^1 \begin{bmatrix}
3 & -2 &6\\
2 & -3 & 4 \\
2 &1 &4
\end{bmatrix} \approx^2 \begin{bmatrix}
1 & 1 &2\\
2 & -3 & 4 \\
2 &1 &4
\end{bmatrix} \approx^3 \begin{bmatrix}
1 & 1 &2\\
0 & -5 & 0 \\
0 &-1 &0
\end{bmatrix} \approx^4 \begin{bmatrix}
1 & 1 &2\\
0 & -1 & 0 \\
0 &-5 &0
\end{bmatrix} \approx^5 \begin{bmatrix}
1 & 1 &2\\
0 & 1 & 0 \\
0 &-5 &0
\end{bmatrix} \approx^6 \begin{bmatrix}
1 & 1 &2\\
0 & 1 & 0 \\
0 &0 &0
\end{bmatrix}$
Rank (A) =2
The rank of each matrix:
$P_{13}$
$A_{21}(-1)$
$A_{12}(-2)$
$A_{13}(-3)$
$P_{23}$
$M_{2}(-1)$
$A_{32}(5)$
