RREF of uneven matrix

I have this matrix:

$$\begin{bmatrix} 3 & 4 & 5 \\ 1 & 2 & 4 \end{bmatrix}$$ Find the RREF

Question: How does RREF work if $m \ne n$ [col =/= rows]

The algorithm is to get the top left to 1 then ignore the top row and leftmost column and the continue, but because this is uneven, I don't see how that works?

• Subtract $2R_2$ from $R_1$. Then subtract $R_1$ from $R_2$. – Chantry Cargill Jan 26 '17 at 22:08
• Your description is pretty straight forward. Where do you get stuck? – user251257 Jan 26 '17 at 22:08
• @user251257 , usually its in the form: $$\begin{bmatrix} 1& 0 \\ 0 & 1 \end{bmatrix}$$, I dont see how to get it here – kalra Jan 26 '17 at 22:11
• @kalra I don't think you understand what RREF is. That's just identity matrix, and while that is in RREF, not all RREF has to be identity. – user160738 Jan 26 '17 at 22:14
• Recall what RREF is for the dummies. Let me guess : the first letters should be Row Reduction ? But the last ones ? – Jean Marie Jan 26 '17 at 22:25

1. Swap R1 and R2: $\quad\begin{bmatrix}1&2&4\\3&4&5\end{bmatrix}$,
2. Subtract 3 R1 from R2: $\quad\begin{bmatrix}1&2&4\\0&-2&-7\end{bmatrix}$,
3. Add R2 to R1: $\quad\begin{bmatrix}1&0&-3\\0&-2&-7\end{bmatrix}$,
4. Divide R2 by $-2$: $\quad\begin{bmatrix}1&0&-3\\0&1&\frac72\end{bmatrix}$.