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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?

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    $\begingroup$ Subtract $2R_2$ from $R_1$. Then subtract $R_1$ from $R_2$. $\endgroup$ – Chantry Cargill Jan 26 '17 at 22:08
  • $\begingroup$ Your description is pretty straight forward. Where do you get stuck? $\endgroup$ – user251257 Jan 26 '17 at 22:08
  • $\begingroup$ @user251257 , usually its in the form: $$\begin{bmatrix} 1& 0 \\ 0 & 1 \end{bmatrix}$$, I dont see how to get it here $\endgroup$ – kalra Jan 26 '17 at 22:11
  • $\begingroup$ @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. $\endgroup$ – user160738 Jan 26 '17 at 22:14
  • $\begingroup$ Recall what RREF is for the dummies. Let me guess : the first letters should be Row Reduction ? But the last ones ? $\endgroup$ – Jean Marie Jan 26 '17 at 22:25
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  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 $-2$: $\quad\begin{bmatrix}1&0&-3\\0&1&\frac72\end{bmatrix}$.
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