Question: 2.20 Let V be the vector space of continuous real-valued functions oft defmed on the interval t e [0, 3] . Let W be the

2.20 Let V be the vector space of continuous real-valued functions oft defmed on the interval t e [0, 3] . Let W be the subspace of V consisting of functions that are linear for 0 < t < 1 , linear for 1 < t < 2 , and linear for 2

a) Construct a basis for W.

b) If an inner product for W is given by

(!,g)= J:f(x)g(x) dx compute the orthogonal projection of f(x) = x2 onto W.

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