# Finding the inverse of a matrix using it's elementary matrix?

• Mar 7th 2011, 05:31 PM
Sherina
Finding the inverse of a matrix using it's elementary matrix?
Hello,

I'm pretty sure this really stupid but I don't fully understand how to do row reduction (Gauss/Gauss-Jordan) to reduce a matrix to 1s and 0s.

(1 4)
(2 7) I know that I'd end up with:

(1 4| 1 0)
(2 7| 0 1) but I'm not sure where to start. Should I try to get a12 to be 0 like ( -7R1 + 4R2)? Will this change the 2nd row determinately? Can I subtract two rows ( R1 - R2)?
• Mar 7th 2011, 05:36 PM
Ackbeet
I usually try to get zero's below the main diagonal first, and then get the zeros above the main diagonal. So my first ERO would be -2 R1 + R2 -> R2.
• Mar 7th 2011, 05:46 PM
Sherina
Quote:

Originally Posted by Ackbeet
I usually try to get zero's below the main diagonal first, and then get the zeros above the main diagonal. So my first ERO would be -2 R1 + R2 -> R2.

What if it was like:

(3 4 1)
(2 -7 -1)
(8 1 5)

Would I try to get a 1 in a11? Is there a general stratagy to reducing something like this?
• Mar 7th 2011, 06:08 PM
Ackbeet
Quote:

Originally Posted by Sherina
What if it was like:

(3 4 1)
(2 -7 -1)
(8 1 5)

Would I try to get a 1 in a11? Is there a general stratagy to reducing something like this?

Good idea; I'd do that first, if I had to reduce to the identity matrix.