Question

Given a matrix w1 and w2 find show that w1 and w2 are subspaces of v . Ii)find the dimensions of w1;w2;w1 +w2 and w1 \w2.

Answer 1

Matrices cannot be spaces (unless it is the zero matrix), so surely you meant W1,W2 sets of all the spaces with the required conditions. I edited your question to clear this out. – DonAntonio Sep 28 '12 at 3:13

Pick a basis for V. See whether, for each A in the basis, you can find B in W1 and C in W2 such that B+C=A. If you can, you have proved the dimension of W1+W2 is 4