(3 points) The function (f, g) = f(-2x(-2) + f(0)g(0) + f(2)g(2) defines an inner product...
Please attempt all questions. 2. Use the polynomial inner product to find the projection of f(*) onto g(x). (a) f(x) = -12 -1, 9(20) = ? (b) f(x) = 2x2, g(x) = 2+1 (C) f(c) = -1-1, g(x) = r2 +3 3. Use the continuous function on the interval [0,1) inner product to find the projection of f(x) onto g(2). (Feel free to use an integral calculator. I use wolfram alpha. Just make sure to type the problem in carefully)....
(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) =
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) =
Please attempt both questions 3. Use the continuous function on the interval (0,1) inner product to find the projection of f(x) onto g(x). (Feel free to use an integral calculator. I use wolfram alpha. Just make sure to type the problem in carefully). (a) f(x) = -22 - 1, g(x) = -2 (b) f(x) = 2r?, g(x) = 2+1 (e) f(x)=-1-1, g(x) = x2 +3 4. Consider 3-space with the dot product. Your subspace S will be the plane z...
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) =
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...
I will upvote! (2)()dz in the vector space Cº|0, 1] to find the orthogonal projection of f(a) – 332 – 1 onto the subspaco V (1 point) Use the inner product < 1.9 > spanned by g(x) - and h(x) - 1 proj) (1 point) Find the orthogonal projection of -1 -5 V = 9 -11 onto the subspace V of R4 spanned by -4 -2 -4 -5 X1 = and X2 == 1 -28 -4 0 -32276/5641 -2789775641 projv...
i need help with this linear Algebra question 4. (6pt) Use the inner product (f,g)f ds to determine the following. (a) Determine if the function g(z) = z2-3x + 2 or h(x) = x2-2x + 1 is closest to the fl () is closest to the function f)2+2 on (b, Show that (1,2r - 1) is an orthogonal set (c) Beginning with the basis (1,2 1, 2 (d) Find an orthonormal basis for P2. (e) Find the least squares quadratic...
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