Let P3 have the inner product given by evaluation at -6, -1, 1, and 6. Let...
Let Ps have the inner product given by evaluation at -2, -1, 1, and 2. Let po(t)-1. P,()-t, and p20)- a. Compute the orthogonal projection of p2 onto the subspace spanned by Po and P1 b. Find a polynomial q that is orthogonal to Po and p,, such that Po P is an orthogonal basis for Span(Po P1, P2). Scale the polynomial q so that its vector of values at a2(Simplify your answer.) Let Ps have the inner product given...
Answer Question #12. Question #11 is only for reference 11. Let po, pi, and p2 be the orthogonal polynomials described in Example 5, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, and 2. Find the orthogonal projection of tonto Span {po, pi, p2). 12. Find a polynomial p3 such that {po, p1, p2.p3} (see Exercise 11) is an orthogonal basis for the subspace P3 of P4. Scale the polynomial p3 so that its...
== Let P3 have the inner product given by evaluation at -3, -1, 1, and 3. Let po(t) = 4, p1(t)=t, and t² – 5 q(t) = Notice that these polynomials form an orthogonal set with this inner product. Find the best 4 approximation to p(t) = tº by polynomials in Span{P0,21,9}. The best approximation to p(t) = tº by polynomials in Span{Po.21,93 is
4 2-5 Notice that these polynomials form an Let P3 have the inner product given by evaluation at -3, -1, 1, and 3. Let po(t) = 2, P (t) = 4t, and act) = orthogonal set with this inner product. Find the best approximation to p(t) = tº by polynomials in Span{Po-P1:9). The best approximation to p(t) = tº by polynomials in Span{Po.P7.93 is
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
Notice that these polynomials form an orthogonal set with this inner product. Find the best 1²-13 Let P2 have the inner product given by evaluation at -5, -1, 1, and 5. Let po(t) = 2, P1(t)=t, and q(t) = 12 approximation to p(t) = t by polynomials in Span{Po.P1,9}. The best approximation to p(t) = t by polynomials in Span{Po.P2,q} is
Let P3 be the vector space of all polynomials of degree 3 or less. Let S = {p1 (t), p2(t), p3 (t), p4(t)}, Q = span{pı(t), p2(t), P3 (t), p4(t)}, where pi(t) =1+3+ 2+2 – †, P2(t) = t +ť, P3(t) = t +ť? – ť, p4(t) = 3 + 8t+8+3. The basis B of Q chosen from the set S is given by: Select one alternative: O pi(t), p2(t), pä(t) Opı(t), p3(t), p4(t) O pi(t), p2(t), pä(t), p4(t) O...
Let R2 have the Euclidean inner product. (a) Find wi, the orthogonal projection of u onto the line spanned by the vector v. (b) Find W2, the component of u orthogonal to the line spanned by the vector v, and confirm that this component is orthogonal to the line. u =(1,-1); v = (3,1) (a) wi = Click here to enter or edit your answer (0,0) Click here to enter or edit your answer (b) 2 = W2 orthogonal to...
please provide step by step solution Thank you (1 point) Use the inner product (5,8) = $* f()g(x) dx in the vector space P(R) of polynomials to find the orthogonal projection of f(x) = 2x2 + 4 onto the subspace V spanned by g(x) = x and h(x) = 1. (Caution: x and 1 do not form an orthogonal basis of V.) projy(f) =
5. Let p and q € P2, and define < p,q >=p(-1)q(-1) + p(0)q(0) +p(1)q(1). (4pts) a. Compute < p,q> where p(t) = 2t – 5t?,q(t) = 4 + t2. (5pts) b. Compute the orthogonal projection of q onto the subspace spanned by p.