# Prove these matricies are not row equivalent for any values of a,b,c

Hello I have two $3\times3$ matrices and need to prove that they are not row equivalent for any values of $a,b,c$ where they are all real numbers

$$\begin{pmatrix} 2 & 0 & 0 \\ a & -1 & 0 \\ b & c & 3 \\ \end{pmatrix}$$ $$\begin{pmatrix} 1 & 1 & 2 \\ -2 & 0 & -1 \\ 1 & 3 & 5 \\ \end{pmatrix}$$

so what is did was I did a bunch of row operation on the second matrix to try and get the first one but since they are supposed to be not row equivalent I couldn't get it. this is the final matrix I got. $$\begin{pmatrix} 2 & 0 & 1 \\ 3 & -1 & 0 \\ 0 & 2 & 3 \\ \end{pmatrix}$$ Since my knowledge on matrices is very limited I have no idea if I am on the right track or not or how I would prove this. Can you help me please?.

On the other hand, if you perform RREF on the second matrix, you will find that it has row rank $2$.