i have the following subspaces:
i need to find the basis for and and to determine if is a direct sum of .
so, this is what i did to find the basis for :
i set in one matrix and found its rank to be 3.
so i can just throw one of this vectors out, and it can be basis for .
and obviously can't be direct sum of , since because .
that all leaves me with 2 questions:
1. first of all: how do i find the basis for ?
2. is it enough to say that " can't be direct sum of , since because " in order to prove that is not a direct sum of ?
thanks in advanced!