2 subspaces of R^4, bases, intersection

Hi MHF,

I appreciate very much all the help I got so far. If I didn't answered my last 2 posts it's because of lack of time. I feel overloaded with linear Algebra and the final exam is coming up next 26th of February.

Here is the exercise I'd like to check out with you.

Let and and let be spanned by and be spanned by .

a)Give a base of contained in , for i=1, 2.

My attempt : I wrote each vector of the base into a matrix as being column vectors and reduced it. I got that 3 of the 4 vectors of were colinear and then I solve a 2 equations system, getting finally that a base of included into is .

Doing the same for , I got that a base of included into is .

b)Describe , , and implicitly.

My attempt : don't know how to start.

c)Give a base of and of .

My attempt : I wrote the bases I got in part a) as vector column in a matrix. I checked out that , hence the matrix is invertible and the 4 vectors are linear independent. So I think that ∅. So there's no base that generates , or I'm wrong?

And as the 4 vectors are linear independent, a basis of would be the union of the bases of and . Or : . Am I right?