# Performing elementary row operations on matrices

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!

• 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. – user84413 Sep 14 '14 at 23:26
• Got it. Nifty way to look at part (b), thanks. – user1282637 Sep 14 '14 at 23:31