# Thread: elementary matrix corresponding to row operations

1. ## elementary matrix corresponding to row operations

I just had a question on my final and i dont remember ever hearing of it(and judging by the fact that 2/3 my class was asking about it im not the only one)

We where required to show the elementary matrix corresponding to each elementary row operation we performed while reducing a matrix ro rref.

for instance what would the elementary matrix be for

| 1 3 | = | 1 3 |
| 3 1 | = | 0 -8| (r2+-3r1)

2. Try:

1 0
-3 1

with this matrix multiplied from the left of your original matrix.

3. Originally Posted by qmech
Try:

1 0
-3 1

with this matrix multiplied from the left of your original matrix.
ah alright thanks

4. Originally Posted by Juggalomike
I just had a question on my final and i dont remember ever hearing of it(and judging by the fact that 2/3 my class was asking about it im not the only one)

We where required to show the elementary matrix corresponding to each elementary row operation we performed while reducing a matrix ro rref.

for instance what would the elementary matrix be for

| 1 3 | = | 1 3 |
| 3 1 | = | 0 -8| (r2+-3r1)
More generally, elementary matrix corresponding to any row operation is the matrix you get by applying that row operation to the identity matrix.

From $\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$, subtracting 3 times the first row from the second gives $\begin{bmatrix}1 & 0 \\ -3 & 1\end{bmatrix}$ as qmech says.

5. Originally Posted by Juggalomike
I just had a question on my final and i dont remember ever hearing of it(and judging by the fact that 2/3 my class was asking about it im not the only one)

We where required to show the elementary matrix corresponding to each elementary row operation we performed while reducing a matrix ro rref.

for instance what would the elementary matrix be for

| 1 3 | = | 1 3 |
| 3 1 | = | 0 -8| (r2+-3r1)

$\begin{pmatrix}1&0\\\!\!\!-3&1\end{pmatrix}$ , multiplication from the left, of course.

Tonio