LINEAR ALGEBRA HELP

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Question:

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T: V V is a linear operator with B and B' ordered bases for V .

a. Find the matrix representation for T relative to the ordered bases B and B' .

b. Find T (v), using a direct computation and using the matrix representation.

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T: P2 P2, T (ax2 + bx + c) = ax2 + bx + c

B = {1, 1 x, (1 x)2 }

B' = {1, x, x2 }

v = x2 3x + 3

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Please explain each step!