Let V P(4) denote the space of quartic polynomials, with the L2 inner product Let W P2 be the subspace of quadratic polynomials (a) Write down the conditions that a polynomial p P(4) must satisfy in order to belong to the orthogonal complement W yen (b) Find a basis for and the dimension of W yen (c) Find an orthogonal basis for W yen P p(x)q(x) dx (p q)

Question: Let V = P(4) denote the space of quartic polynomials, with the L2 inner product Let W = P2 be the subspace of quadratic polynomials.

Let V = P(4) denote the space of quartic polynomials, with the L2 inner product

Let W = P2 be the subspace of quadratic polynomials.
(a) Write down the conditions that a polynomial p ˆŠ P(4) must satisfy in order to belong to the orthogonal complement WŠ¥.
(b) Find a basis for and the dimension of WŠ¥.
(c) Find an orthogonal basis for WŠ¥.

P p(x)q(x) dx. (p.q) =

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