Meticulously show that if V is a vector space with zero vector 0 and we V satisfying kw = 0 for k # 0, then w = Q

Meticulously show that if V is a vector space with zero vector 0 and we V satisfying kw = 0 for k # 0, then w = Q. (Be sure to identify all the axioms/properties that you are using) Question 9 Let V = R1 = {(x, y, z, w) : r, y, z, we R} . For each of the following, deter- mine a basis and the dimension of the subspace of R that is spanned by the given set. (i) W1 = {(a, b, c, d) ( R' : b - 2c + d = 0} (ii) W2 = {(a, b, c, d) ( R' : a = d and b = 2c}. (iii) WinW2. Question 12 Find the dimension of the subspace of R3 spanned by