Factorise matrix determinant How do I reduce this matrix to row echelon form and hence factorise the determinant, or is there a way that I am unaware of that factorise the determinant of this matrix without having to reduce it row echelon form given this is all I know and there exists no additional information.
$\left[
  \begin{array}{ccc}
    y+z+2x & y & z \\
    x & z+x+2y & z \\
    x & y & x+y+2z \\
  \end{array}
\right]$

$C_1\to C_1+C_2+C_3$. Take common from $C_1$. Then $R_2\to R_2-R_1$ and $R_3\to R_3-R_1$. Then   open along $R_1$. You will just have to multiply $2$ equal terms whn expanding.
