Question

Let T : R2 ! R2 be a linear transformation that transforms the vector ~e1 into [1 3] andthe vector ~e2 into [2 4].
(a) Find the standard matrix of T.
(b) Find the image of the vector ~c =[1 2] under T.
(c) Find a linear transformation S : R2 -> R2 such that S(T(~x)) = ~x for all ~x (S is
called the inverse of T, denoted T^-1).