Question

(1 point) Use the inner product 1 0 <fig >= f(x)g(x)dx in the vector space Cº[0, 1] to find the orthogonal projection of f(x) = 6x2 + 1 onto the subspace V spanned by g(x) = x – į and h(x) = 1. projy(f) =

Answer 1

orthogon al pegection of R onto the subspace spanned by f heals = 1 het free) = 6*1²+1 gcse) = &- £ is given by < fed af, h> gezes and heses + b 11 112 proj,(f) 119112 da I fla) gree) Here afises, geres jen l'ex’rajce-4a) do gew-sex-toy de *]d! x4 Lp 11 [ 3, (094 + (0 % - %(-07 New -1+1-1] 1 w goes v* = SGeory zde 0 0 <foe, gox)) = ? fem-1a7203 14***+% de = [ 14- *****] - [9] = *** igræ3112 (cuܬ + 금

1 fca) has da Lf (x), heas) = s'c 6221) a da 0 s(6x²+1) dx o [20113 +(1)] [6 x + a)! 2+) j'adx sluneda < fral), h(x) >= 3 |(21x)} Bila 116180112 0 [*],'- 11-01-1 در زد ۱۱۸ . vallees in egno all these putting efine h 14197 7 + 11h 112 Projulfo ''2112 %10) 12 mg-12) 112 6(x-1/2) +3 62-3+3 62 projvlf) = BX