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Suppose you’re doing elementary row operations on matrices which have real entries and have 3 rows.

(a) Write down the elementary matrix which correspond to the elementary row operation r3 → r3 + π · r2.

(b) What elementary row operation is performed by left multiplying by the following elementary matrix?

$$ \begin{matrix} 1 &0 &0 \\ −5 &1 &0 \\ 0 &0 &1 \\ \end{matrix} $$

To find (a), would I just do the row operation r3 → r3 + π · r2 on the 3x3 identity matrix?

For (b), any guidance would be helpful.

Thanks!

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    $\begingroup$ Your idea for a) is correct, and for b) see what happens if you write the 3x3 matrix as $\begin{bmatrix} r_1\\r_2\\r_3\end{bmatrix}$ and then left-multiply by the given matrix. $\endgroup$ – user84413 Sep 14 '14 at 23:26
  • $\begingroup$ Got it. Nifty way to look at part (b), thanks. $\endgroup$ – user1282637 Sep 14 '14 at 23:31
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(a) Correct.

(b) r2=r2-5*r1

Try it out by left-multiplying the matrix in (b) to an arbitrary/anonymous 3x3 matrix. You will be able to verify that above is correct and know why it should be the case as you try the multiplication.

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