I need help with this problem
Let V be a vector space over the field of complex numbers, and suppose there is an isomorphism T of V onto C^3. Let a1, a2, a3, a4 be vectors in V such that
Ta1= (1,0,i) Ta2= (-2, 1+i, 0) Ta3=(-1,1,1) Ta4 = (root 2, i, 3)
a) Is a^1 in the subspace spanned by a2 and a3? (I've already done this)
b) Let W^1 be the subspace spanned by a1 and a2, and let W2 be the subspace spanned by a3 and a4. What is the intersection of W1 and W^2? For this, how do I find the intersection of the two subspaces, after finding the vectors in the subspaces they span?
c) Find a basis for the subspace of V spanned by the four vectors a1, a2, a3, a4. Do I find this by finding the basis for the subspace of C^3 spanned by the four Ta vectors? Thanks