For a homework problem, I am required to find an elementary matrix E whcih will be able to perform the row operation R2 = -3R1 + R2 on a matrix A of size 3x5 when multiplied from the left, i.e. EA. I am also required to show my method on how I got E. My problem is that I have not seen a problem like this before and I'm not really sure where to start. I initially came up with a matrix that would require me to perform such a row operation to get it into RREF, but I don't think that's what this problem is looking for. Any help would be appreciated!
2026-04-24 14:29:42.1777040982
Find elementary matrix E
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Let $I_{rs}=\begin{pmatrix} 0 & 0 & \cdots & 0 \\ \vdots & 0 & 1 & \cdots \\ 0 & \cdots & 0 & \ddots \end{pmatrix}$
so the only non-zero entry of $I_{rs}$ is placed at r th row and s th column.$I_{rs}A$ simply places s th row at r th row and makes all other entries zero so we can say that
$(I+cI_{rs})A$ changes r th row $R_r$ with $cR_s+R_r$ and doesn`t affect other rows.
The row operation which you want to find is $I-3I_{21}$