Question

9. We know from the last homework that the angle between l;(x) = x3 and lt1() basis to construct an orthogonal basis for a polynomial space over the domain 0, 1 not perpendicular. However, we can use this е lo(x). Compute the projection of (a) Let go(r) and call it w(x) (x) onto span{go(ar)}, (b) Сompute q. (") — 6, (ӕ) — w;(»). (c) Compute the projection of l2(x) onto span{go(x), q1 (x)}, and call it w2(x) (d) Compute 2(x)= l2(x) - w2(x) (e) Explain why {go(x), qı (x), q2(x)} forms an orthogonal basis for quadratic polynomials

Answer 1

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