Hi everyone,

I've just got a question today. I've given it a few attempts, but I keep getting stuck, and I'm not sure where I'm going wrong.
Let S and T be subspaces of

, where:

S is generated by the matrices

, where

and T is generated by the matrices

, where

.

I've already done the first part of the question, determining dim(S) and dim(T) [Just had to prove the matrices contained are linearly independent.]

The part I need help with is determining the basis and dimension of

.

I've tried creating a spanning set, and then proving that they're linearly independent, and it indicates that they are. Which doesn't make sense, because then it implies that the dimension theorem is wrong.

I figure I'll throw it out there, I can't find any examples on the internet for anything similar, and I'm only getting more confused.