5. Let p and q € P2, and define < p,q >=p(-1)q(-1) + p(0)q(0) +p(1)q(1). (4pts)...
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...
Let P3 have the inner product given by evaluation at -6, -1, 1, and 6. Let po(t) = 1, p1(t) = 2t, and P2 (t) = ? a. Compute the orthogonal projection of P2 onto the subspace spanned by Po and P4. b. Find a polynomial q that is orthogonal to po and p1, such that {PO,P1,93 is an orthogonal basis for Span{PO,P1.P2}. Scale the polynomial q so that its vector of values at ( - 6, - 1,1,6) is...
Please write/type clearly. (1 point) Use the inner product < p, 2 >= P(-2)(-2) + p(0)q(0) + p(3)q(3) in P3 to find the orthogonal projection of p(x) = 3x2 + 6x – 8 onto the line L spanned by q(x) = = 2x2 – 3x – 9. projų (p) =
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
What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p of the vector b-5 onto this subspace? Pi P2 Ps What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p...
(1 point) Use the inner product <p.q >= P(-3)(-3) + p(0)q(0) + p(2)q(2) in Pg to find the orthogonal projection of p(x) = 2x2 + 6x + 4 onto the line L spanned by 9(x) = 3x2 - 4x - 6. proj. (p) =
(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) =
Let H be a separable Hilbert space with basis {en}neN and define P2 as the orthogonal projection onto spanfe1,., e,}. Show that, for any T E B (H), the sequence PTP converges strongly to T HINT: A sequence of operators Tn E B (H) converges strongly to T if ||Th - Tnh|| converges to 0 Vh E H. Let H be a separable Hilbert space with basis {en}neN and define P2 as the orthogonal projection onto spanfe1,., e,}. Show that,...
Define four sets of integers Let P {0, 1), let Q {-11, 1, 5) , and Let R and S be arbitrary nonempty subsets of Z. Define an even indicator function F F: ZP by F(x) = (x + 1) mod 2 for x e Z That is, F(x) 1 if x is even, and F(x) = 0 if x is odd. or neither? Explain. a) Is F: Q P one-to-one, onto, both, or neither? Explain. b) Is F: (Pn...
Problem 7. Let P R2 -> R2 be the orthogonal projection onto the line Li Let P2 R2 R2 be the orthogonal projection onto the line L2: x32 2r2 0. 0. (1) What are the image and kernel of P2P What is the rank of P2P? Give a geometric description, without relying on the matrix of P2P (2) Find the matrix that represents P2P Problem 7. Let P R2 -> R2 be the orthogonal projection onto the line Li Let...