# Finding the elementary matrix

• May 16th 2011, 09:55 AM
crakapete
Finding the elementary matrix
Write down the elementary matrix E such that the matrix EA is obtained from A when:

the third row of A is replaced by (row three of A - 2 x row one of A ).

So I dont know where to start with this. I tried Letting A equal an example matrix, Then EA = The matrix after the stated operation. Then E = A/EA and therefore
E = (EA)^-1 (A). Am I on the right track? Unfortunately I dont think my EA matrix was even invertible. Im lost! :(

Any help is much appreciated.
• May 16th 2011, 03:52 PM
Turiski
Are you on the right track? Possibly, but you seem to me making it a bit hard on yourself. I don't really remember what elementary matrices are but you should be able to do what the problem asks by considering how matrices take linear combinations of rows when multiplied on the left.

Aaaand after a quick trip to Wikipedia, the matrix you'll get by doing that will be an elementary matrix, so if you can do that, you're golden.
• May 16th 2011, 05:41 PM
Lord Darkin
Multiplying negative 2 to the second row, and adding it to the third, yields:

1 0 0
0 1 0
0 -2 1
• May 17th 2011, 01:19 AM
crakapete