Matrix Space, dependence/indepence (HELP)

[Noxide]

Homework Statement

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]

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

 

[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.

 

[Noxide]

lol
thanks!