Question: Show that S = {x 2 + 3x 2, 2x 2 + 5x 3, x 2 4x + 4} is a basis

Show that S = {x2 + 3x − 2, 2x2 + 5x − 3, −x2 − 4x + 4} is a basis of P2(R). Recall that for a basis, you need to show

(i) span(S) = P2(R) and

(ii) S is linearly independent.

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