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please provide step by step solution Thank you (1 point) Use the inner product (5,8) =...
(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) =
Section 5.5 Orthonormal Sets: Problem 6 Previous Problem Problem List Next Problem 1 (1 point) Use the inner product < f, g >= . f(x)g(x)dx in the vector space C°[0, 1] to find the orthogonal projection of f(x) = 6x2 + 1 onto the subspace V spanned by g(x) = x - and h(x) = 1. projy(f) =
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)....
(3 points) The function (f, g) = f(-2x(-2) + f(0)g(0) + f(2)g(2) defines an inner product on P2. With respect to this inner product, find the orthogonal projection of /)-4x2 +5x-3 onto the subspace L spanned by g(x) = 2x2-2x-4.
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...
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...
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...
Could someone give me the definitions for these ? You don't need to go into details. just a brief def would do. and pls answer ALL. Thank you Definitions for The abstract definitions of 0 and -in a vector space. - Kernel and image of a linear transformation Span, linear independence, subspace, basis, dimension, rank in the context of an abstract vector space Coordinates of a "vector" with respect to a basis Matrix of a linear transformation with respect to...
Problem 4. Let V be the vector space of all infinitely differentiable functions f: [0, ] -» R, equipped with the inner product f(t)g(t)d (f,g) = (a) Let UC V be the subspace spanned by B = (sinr, cos x, 1) (you may assume without proof that B is linearly independent, and hence a basis for U). Find the B-matrix [D]93 of the "derivative linear transformation" D : U -> U given by D(f) = f'. (b) Let WC V...
Problem 1. Let the inner product (,) be defined by (u.v)xu (x)v (x) dx, and let the norm Iilbe defined by lIul-)Corhe target funtio), and work with the approximating space P4 Use Gram-Schmidt orthogonalization with this inner product to find orthogonal polynomials (x) through degree four. Standardize your polynomials such that p: (1) 1. (a) Form the five-by-five Gram matrix for this inner product with the basis functions p (x) degree 4 approximation o f (x) using the specified norm,...