prove and please explain it with steps

Exercises 29-34 require knowledge of the sum and direct sum of subspaces, as defined in the exercises of Section 1.3. 29. (a) Prove that if W, and W2 are finite-dimensional subspaces of a vector space V, then the subspace W1 + W2 is finite-dimensional, and dim(W1 + W2) = dim(W1 ) + dim(W2) - dim(WinW2). Hint: Start with a basis {u1, u2, ..., uk} for WI n W2 and extend this set to a basis {u1, u2, . . ., Uk, V1, U2, . .., Um} for Wj and to a basis {u1, U2, . . ., Uk, W1, W2, . .., Wp } for W2. (b) Let W, and W2 be finite-dimensional subspaces of a vector space V, and let V = W1 + W2. Deduce that V is the direct sum of W and W2 if and only if dim(V) = dim(W1 ) + dim(W2)