# Homework Help: Matrix Space, dependence/indepence (HELP!)

1. Oct 22, 2009

### Noxide

1. The problem statement, all variables and given/known data

Is this set of 2x2 matrices linearly independent or dependent in M2,2 (the space of 2x2 matrices)

Matrix 1 (2x2)
[ 1 4 ]
[ -1 3 ]

Matrix 2 (2x2)
[ -1 5]
[ 6 2]

Matrix 3 (2x2)
[ 1 13]
[ 4 7]

3. The attempt at a solution

I know that I need to set r1M1 + r2M2 + r2M3 = 0

and then make some equations = 0
then put those in a matrix
make that matrix part of a linear system
do row reduction
if trivial solutions exist then it's independent
if trivial solutions don't exist

I HAVE NO CLUE HOW TO DO THE FIRST STEP THOUGH, never seen an example with matrices. HELP!

2. Oct 22, 2009

### LCKurtz

You know that a constant times a matrix multiplies each element of the matrix, right?

And in your equation r1M1 + r2M2 + r3M3 = 0 the zero in the right side is the zero matrix, right? So write out the matrix equation you get and equate the elements.

3. Oct 22, 2009

lol
thanks!