Let W be a subset of R^3 with elements (x,y,z) that satisfy:

a1x + a2y + a3z = 0

b1x + b2y + b3z= 0

for some ai and bj with at least one ai and one bj non-zero. Prove that W is a subspace of R^3. Find the dimension of W if:

a) a1/ b1 = a2/ b2 = a3/ b3

b) if all the above proportions are not equal.