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Let P2 be the vector space of all real polynomials of degree at most 2...

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Let P2 be the vector space of all real polynomials of degree at most 2 Let P P2 P3 E P2 be given by pi z 2 p2 x 2x x and p3 x x ar a 4 marks Find the condition on a ER that ensures that P1 P2 P3 is a basis for P2 You are free to assume that the polynomials 1 2 and are linearly independent b 2 marks In the case that a 4 write the polynomial p x 4 write the polynomial p x combination of p1 p2 and p3 Can you write the polynomial p x 2 r r as a linear combination of p p2 and P3 when a Justify your answer 2 1 as a linear

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