Answer
The elementary matrices are $A_{23}(2),M_2( -1),A_{13}(-3),A_{12}(-2)$
Work Step by Step
We can reduce A to row-echelon form using the following sequence of elementary row operations:
$\begin{bmatrix}
1&2 & 3 & 4\\
2& 3 & 4 & 5\\
3 & 4 &5& 6
\end{bmatrix} \approx^1\begin{bmatrix}
1&2 & 3 & 4\\
0& -1 & -2 & -3\\
0 & -2 &-4& -6
\end{bmatrix} \approx^2\begin{bmatrix}
1&2 & 3 & 4\\
0& 1 & 2 & 3\\
0 & -2 &-4& -6
\end{bmatrix} \approx^3 \begin{bmatrix}
1&2 & 3 & 4\\
0& 1 & 2 & 3\\
0 & 0 &0&0
\end{bmatrix}$
$1.A_{12}(-2)$
$3.A_{13}(-3)$
$4.M_2(-1)$
$5.A_{23}(2)$
So, elementary matrices are $A_{23}(2),M_2( -1),A_{13}(-3),A_{12}(-2)$
