Suppose T: ℝ2→ℝ3 is a linear transformation. Let U, V and W be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(W).

U = [1, 1]^T
V = [3, 4]^T
W = [-10, -13]^T
T(U) = [0, 0, 1]^T
T(V) = [-5, -2, 6]^T