Suppose that T ∈ £(R"; R'") for some n,m ∈ N.
a) If T(l, 1) = (3, π, 0) and T(0, 1) = (4,0, 1), find the matrix representative of T.
b) If T(l, I, 0) = (e, π), T(0,-1, 1) = (1, 0), and T(l, 1,-1) = (1.2), find the matrix representative of T.
c) If T(0, 1, 1, 0) = (3, 5), T(0, 1, -1, 0) = (5, 3), and T(0, 0, 0, -1) = (π, 3), find all possible matrix representatives of T.
d) If T(l, 1, 0, 0) = (5, 4, 1), T(0, 0, 1, 0) = (1. 2, 0), and T(0, 0, 0, -1) = (π, 3, -1), find all possible matrix representatives of T.