Use Gaussian elimination to convert matrix A to row echelon form R.

Can someone please help me with this question if you can? I have done the ERO's, but I did 5 instead of the 3 that it is asking for and I cannot seem to get it down to 3. I'm not sure if I am reading it wrong or if I just can't figure out how to only do 3 ERO'S. :/ Thank you!

Use Gaussian elimination to convert $$A = \begin{pmatrix} 1 & 1 & 0 \\ 4 & 6 & 1 \\ -2 & 2 & 0 \\ \end{pmatrix}$$ to row echelon form $R$. Write the three elementary row operations as 3-by-3 matrices, $E_1$, $E_2$, $E_3$, so $E_3E_2E_1A=R$. Multiply these three matrices to determine $M = E_3E_2E_1$, a single matrix that performs all the elimination steps (i.e., $MA=R$).

1 Answer

$$\pmatrix{1 & 1 & 0 \\ 4 & 6 & 1 \\ -2 & 2 & 0} \sim \pmatrix{1 & 1 & 0 \\ 0 & 2 & 1 \\ -2 & 2 & 0} \sim \pmatrix{1 & 1 & 0 \\ 0 & 2 & 1 \\ 0 & 4 & 0} \sim \pmatrix{1 & 1 & 0 \\ 0 & 2 & 1 \\ 0 & 0 & -2}$$

Three moves to get to row echelon form. Now just construct the matrices.