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Vector space of polynomials of degree

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Reference no: EM131428254

Let V = P5, the vector space of polynomials of degree ≤ 5, with coefficients in R, and let W = { p(x) ∈ P5 | p(0) = p(1) = p(2) }

1) Show that W is a subspace of V 

2) Let u(x) = x(x - 1)(x - 2), and explain why for every q ∈ W there exists r ∈ P2 such that q(x) = u(x) · r(x) + q(0).

3) Find a basis B for W and order it by increasing degree.

4) For u as in part (2), find the coordinate vector [u]B of u with respect to B from part (3).

Reference no: EM131428254

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