are subspaces of R^4. Determine whether the sum U+W is direct and find dim(U+W).
I find it is not direct since, for example, (1,1,1,0) is a member of both.
Now for the second part I use theorem Dim(U+W)=dim(U)+dim(W)-dim('union'))
I know dim(U) and dim(W) as I earlier calculated basis for them but how do I find the dimension of the union?