# Finding a row-reduced echelon matrix such that R=PA

I need find a row-reduced echelon matrix R which is row equivalent to A and an invertible 3×3 matrix P such that R=PA. I have all the elementary matrices and when multiplied together I get P, but when I multiply PA it does not equal R. Did I write out the elementary matrices incorrectly ?

This is what I have done

• That paper's a little too hard for me to read. I realize it'd be a lot of work to type it all out, but if you decide to, the way to render $$\pmatrix{a & b \\ c & d} \stackrel{R_2 \to R_2 - \frac {c}{a}R_1}\longrightarrow \pmatrix{a & b \\ 0 & d-\frac{bc}{a}}$$ is to type $$\pmatrix{a & b \\ c & d} \stackrel{R_2 \to R_2 - \frac {c}{a}R_1}\longrightarrow \pmatrix{a & b \\ 0 & d-\frac{bc}{a}}$$. – user137731 Oct 6 '15 at 3:20
• I uploaded a clearer image, hopefully it is easier to read now – user273323 Oct 6 '15 at 3:46
• It looks like $P_6$ and $P_7$ are wrong. You should be ADDING multiples of row 3 to the other rows, not subtracting. – Alex Zorn Oct 6 '15 at 3:53