# Subtracting rows to get the Row Echelon Form of a matrix.

So I was taught that to get the Row Echelon Form of a matrix you have to add, subtract, or multiply the rows. So if I have a matrix like \begin{bmatrix}1&0&0\\1/2&1/2&-1/2\\1/2&-1/2&1/2\end{bmatrix} And I want to make the last two rows in column one zero then could I subtract row two and three and change both rows or can I only change one row when I subtract?

What you are allowed to do is to replace a certain row with the result of adding or subtracting a multiple of another row. In your example, you could naturally use row 1, so you replace R2 with R2-R1, and R3 with R3-R1: $$\begin{bmatrix}1&1&1\\0&0&-2\\0&-2&0\end{bmatrix}.$$
• It doesn't really matter which row you use. If you already have a $1$, you usually want to use that row. If you don't, you'll have to divide some row by a number to get a $1$. – Martin Argerami Sep 25 '16 at 5:01