The problem reads as follows:
Let V be a vector space of dimension n. Let be a subspace of dimension . Let be a subspace of dimension . Prove that if , then:
The hint says to argue by contradiction. So we assume . So if that's the case, since dimension is non-negative. It now says to use the concept of dimension to produce the contradiction. Here's where I'm getting stuck.
So how does that use the contradiction we've established? Can you clarify?
Also, we haven't gotten that far in the class to show that equation you used, so I would have to show that too somehow.
I'll ask him when we get done with spring break, but something tells me that's not what the professor wants (i.e. is there another way of doing it?).