Answer
See answers below
Work Step by Step
$\begin{bmatrix}
1 & -1 & -1 &2\\
3& -2 & 0 & 7\\
2 & -1 & 2 & 4\\
4 & -2 & 3 & 8
\end{bmatrix} \approx^1\begin{bmatrix}
1 & -1 & -1 &2\\
0& 1 & 3 & 1\\
0& 1 & 4 & 0\\
0 & 2 & 7 & 0
\end{bmatrix} \approx^2 \begin{bmatrix}
1 & 0 & 2 &3\\
0& 1 & 3 & 1\\
0& 0 & 1 & -1\\
0 & 0 & 1 & -2
\end{bmatrix} \approx^3 \begin{bmatrix}
1 & 0 & 0 &5\\
0& 1 & 0& 4\\
0& 0& 1 & -1\\
0 & 0 & 0 &-1
\end{bmatrix} \approx^4 \begin{bmatrix}
1 &0 & 0 &5\\
0& 1 & 0 & 4\\
0& 0 & 1 & -1\\
0 & 0 & 0 & 1
\end{bmatrix} \approx^5 \begin{bmatrix}
1 & 0 & 0 &0\\
0& 1 & 0 & 0\\
0& 0& 1& 0\\
0 &0 &0 & 1
\end{bmatrix}$
Rank (A)= 4
The last matrix is in a row-echelon form.
$A_{12}(-3),A_{13}(-2),A_{14}(-4)$
$A_{21}(1),A_{23}(-1), A_{24}(-2)$
$A_{31}(-2),A_{32}(-3), A_{34}(-1)$
$M_4(-1)$
$A_{41}(-5),A_{42}(-4), A_{43}(1)$
