# Determining whether sets of matrices in a vectorspace are linearly independent?

1. ### n00bot

11
Given matrices in a vectorspace, how do you go about determining if they are independent or not?

Since elements in a given vectorspace (like matrices) are vector elements of the space, I think we'd solve this the same way as we've solved for vectors in R1 -- c1u1 + c2u2 + c3u3 = 0. But I'm not sure I'm setting it up right. I assume that three 2x2 matrices in r2, for example: (a,b;c,d), (e,f; g,h), (i,j;k,l) where a semi-colon denotes a new line, would be set up like this:

a e i
b f j
c g k
d h l

Am I understanding this correctly?

2. ### tiny-tim

26,053
hi n00bot!

yes, that's correct

checking independence only involves scalar multiplication,

so the matrix structure is irrelevant, and you can treat the matrix components as if they were just vector components

3. ### n00bot

11
OK, great! Thanks very much for the explanation :)