# elementary matrix corresponding to row operations

• Mar 29th 2010, 12:31 PM
Juggalomike
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)
• Mar 29th 2010, 02:18 PM
qmech
Try:

1 0
-3 1

with this matrix multiplied from the left of your original matrix.
• Mar 29th 2010, 04:35 PM
Juggalomike
Quote:

Originally Posted by qmech
Try:

1 0
-3 1

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

ah alright thanks
• Mar 30th 2010, 03:06 AM
HallsofIvy
Quote:

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.
• Mar 30th 2010, 04:31 AM
tonio
Quote:

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