1. Consider the transformation T : P2 R3 dened by T (p(t)) = p(0), p(1), p(2) (3x1 matrix) 1a. Show that

1. Consider the transformation T : P2 → R3 defined by T (p(t)) =  p(0), p(1), p(2)   (3x1 matrix)

1a. Show that T is a linear transformation.

1b. Find the matrix for T relative to the bases B and E where B = {1, t, t2} and E = {e1, e2, e3}.

1c. Find a basis for the kernel of T . (Hint: this is another name for the null-space of the transformation.)

1d. Find the dimension of the range of T , and briefly explain why this is the same as the rank of the matrix you found in 1b.