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
S is generated by the matrices
and T is generated by the matrices
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.