# Simple Isomorphism question

## Homework Statement

Let V be a vector space over the field of complex numbers, and suppose there is an isomorphism T of V onto C3. 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 = (2^1/2, i, 3)

Let W1 be the suubspace spanned by a1 and a2, and let W2 be the subspace spanned by a3 and a4. What is the intersection of W1 and W2?

## The Attempt at a Solution

In this problem, can we find numerical values for the intersection of the given two subspaces? It's obvious that the intersection would be a line passing through the origin, but given no numerical values of a1,2,3,4 in V, can we find a single vector that spans the line?