Hi.

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!