Question: 1. Consider the transformation T : P2 - R3 defined by P(0) T(p(t)) = p(1) P(2) la. Show that T is a linear transformation. 1b.

1. Consider the transformation T : P2 - R3 defined by P(0) T(p(t)) = p(1) P(2) la. Show that T is a linear transformation. 1b. Find the matrix for T relative to the bases B and & where B = { 1, t, to } and & = {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

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