Let T: P3 → P₂ be the linear transformation given by 2 T(p(x))= dp(x) dx where P3 and P2 are the spaces of polynomials of degrees at most 3 and 2 respectively. Find the matrix representative of T relative to the bases {x³, x², x, 1} and {x², x, 1} for P3 and P₂.

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