Finding Elementary Matrices

• March 6th 2011, 02:32 PM
divinelogos
Finding Elementary Matrices
Problem:

Determine elementary matrices that reduce the given matrix to row-echelon form.

$\left[\begin{array}{ccc}
5 & 8 & 2\\
1 & 3 & -1\end{array}\right]$

Question:

Given that elementary matrices are obtained by performing ERO's on the identity matrix, what identity matrix is going to be used in this situation? The identity matrix is nxn, but this given matrix is mxn.
• March 7th 2011, 02:01 AM
Ackbeet
Technically, you have two choices: left-multiply with 2 x 2 elementary matrices, or right-multiply with 3 x 3 elementary matrices. I would definitely go with the first option, because right-multiplication is a lot less familiar to me. But you can do as you choose, obviously.