Question

Score: 0 of 2 pts 4 of 6 (4 complete) HW Score: 20%, 4 of 20 pts 6.7.7 Question Help This exercise refers to P, with the inner product given by evaluation at - 1,0, and 1. Compute the orthogonal projection of q onto the subspace spanned by p, for p(t) = 6 +t and g(t) = 6 -5t2 The orthogonal projection of q onto the subspace spanned by p is

Answer 1

ANSWER:

o Given P(t) = 6+t , qlt) = 6-51² at to = -1, t, -0,2 = 1 Here, we have to find the orthogonal projection of q on to Subspace Spanned by p is Projp (2) . <P,q>P LP.P> where rs EP eris) = rcoss (0) +861)(1) + 86-156-1) P(t) = 6+t qlt) = 6-57? C.P, q> = P(0) 9 (0) +P (1) 9 (1) + P(-1)91-1) (670)(6-560)) +(6+1)(6-561)2)+(6+(-1)) (6-50-1127 (6)(6)+(7)(1) +15)(0) 36+7+5 CP:q> .48 LP.p> - POPCO) + PO1P () + P(-1) P(-1) (6+0)(6+0) + (6+1)(6+1)+(6+(-1)) (6+(-1)) (6)(6) + ( +)(7) + (5)(5)

36 +49 +25 KP, p> = 110 Now, <P, q>P Proj P C). <PP> 48(6++) 110 288 ust + 110 110 144 + 24 55 t 55 Therefore, The orthogonal projection of q onto the 144 Subspace spanned by p is 24 t 55 55