\begin{bmatrix}1&2\\2&0\\3&0\end{bmatrix}
I am trying to use Gaussian elimination to get reduced row echelon form but I'm not sure whether my steps are correct. This is what I did:
\begin{bmatrix}1&2\\2&0\\3&0\end{bmatrix}
-> \begin{bmatrix}1&2\\2&0\\1&0\end{bmatrix}
-> \begin{bmatrix}1&2\\1&0\\1&0\end{bmatrix}
-> \begin{bmatrix}1&2\\1&0\\0&0\end{bmatrix}
-> \begin{bmatrix}1&2\\0&-2\\0&0\end{bmatrix}
At this point, can I just divide row 2 by -2 to get a nice 1 over there? is that allowed?
Best Answer
Yes this is totally legal. Recall that you can multiply by a scalar. In the context of dividing by a scalar you are really just multiplying by some scalar 1/n