Answer
See answers below
Work Step by Step
$\begin{bmatrix}
3 & 7 & 10\\
2 & 3& -1 \\
1 & 2 &1
\end{bmatrix} \approx^1\begin{bmatrix}
1 & 2 & 1\\
2 & 3& -1 \\
3 & 7 &10
\end{bmatrix} \approx^2 \begin{bmatrix}
1 & 2& 1\\
0 & -1& -3 \\
0 & 1 &7
\end{bmatrix} \approx^3 \begin{bmatrix}
1 & 2& 1\\
0 & 1& 3 \\
0 & 1 &7
\end{bmatrix} \approx^4 \begin{bmatrix}
1 & 0& -5\\
0 & 1& 3 \\
0 & 0 &4
\end{bmatrix} \approx^5 \begin{bmatrix}
1 & 0& -5\\
0 & 1& 3 \\
0 & 0 &1
\end{bmatrix} \approx^6 \begin{bmatrix}
1 & 0& 0\\
0 & 1& 0 \\
0 & 0 &1
\end{bmatrix} $
Rank (A)= 3
The last matrix is in a row-echelon form.
$P_{13}$
$A_{12}(-2), A_{13}(-3)$
$M_2(-1)$
$A_{21}(-2),A_{23}(-1)$
$M_3(\frac{1}{4})$
$A_{31}(5), A_{32}(-3)$
