Given p₁ = 1 + 2x + x², P₂ = 2 +9x, and p3 = 3 + 3x + 4x², i. show that the set S = {P₁, P2, P3} is a basis for P₂. ii. express p = 2 + 17x - 3x² as a linear combination of the vectors in S. iii. find the coordinate vector of prelative to S.

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