Can the steps used to solve for the Echelon form result in different answers, or will they always yield the same answer?

Question

Starting Matrix: A= \begin{pmatrix}3 & -4 & 0 & 9\\ 2 & 4 &-1 & 0\\ 10 & 0 &-2 & -4 \end{pmatrix}

Given = \begin{pmatrix}1 & 0 & -1/5& 0\\ 0 & 1 &-3/20 &0\\ 0 &0 & 0 & 1\end{pmatrix} My answer : = \begin{pmatrix} 1& 0& -1/5& -2/5\\ 0 & 1 &-3/20 &-9/10\\ 0 &0 & 0 & 1\end{pmatrix}

why my answer is different?Ive rechecked it alot of time Ive solved it correctly

Answer 1

You can continue the process : the third line can be used to delete both last entries in your second and first lines. You have to do the following : $L_2 \leftarrow L_2 + \frac{9}{10} L_3$ and $L_1 \leftarrow L_1 + \frac{2}{5} L_3$. You will then get the correct answer.