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?
[Math] Subtracting rows to get the Row Echelon Form of a matrix.
linear algebramatrices
Best Answer
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: $$ \begin{bmatrix}1&1&1\\0&0&-2\\0&-2&0\end{bmatrix}. $$