Consider the linear transformation T: R ? R defined by T(x, y, z) = (y, y + 2z, 3x + y ? 2z).Part(a)[3 points] Find

Consider the linear transformation T: R³ ? R³ defined by T(x, y, z) = (y, y + 2z, 3x + y ? 2z).Part(a)[3 points] Find the standard matrix of T.Part(b)[12 points] Show that I is invertible and then find the vector T-¹(x, y, z).Part(c) [3 points] Find the pre-image of (3, 4, -1) under T.