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5. Consider the following basis for P: B = {1,3+20+2=+2x"} Consider the inner product (p, q)...
4) Consider the inner product space P2(R), with inner product (a) Use the Gram-Schmidt process to...
4) Consider the inner product space P2(R), with inner product (a) Use the Gram-Schmidt process to construct an orthonormal basis from the basis (b) Using your answer to part (a), give the least squares approximation in P2(R) to the function f(x)on the interval [0, 1. Hint: You may use the following result without proof f Ine* dr = (-1)"(ane-n!), where ao = 1, an- | n. + | , for n-1, 2, ).
4) Consider the inner product space P2(R),...
Use the Gram-Schmidt process to transform the basis, B = {(1,2), (3, 4)} for R² into...
Use the Gram-Schmidt process to transform the basis, B = {(1,2), (3, 4)} for R² into (a) an orthogonal basis for R and (b) an orthonormal basis for R using the Euclidean inner product; that is, dot product, and use vectors in the order in which they are given.
(4) Consider the inner product space P2(R), with inner product (a) Use the Gram-Schmidt process t...
(4) Consider the inner product space P2(R), with inner product (a) Use the Gram-Schmidt process to construct an orthonormal basis from the basis 11, r, r2) b) Using your answer to part (a), give the least squares approximation in P2(R) to the function f(x) e on the interval [0, Hint: You may use the following result without proof: J İlne dra(-1)"(ane-n!), where ao-1, an-le! + îl , for n-1, 2, or n=1,2 .. ).
(4) Consider the inner product space...
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of co...
NEED (B) AND (C)
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of continuous real-valued funo- tions on the domain [-1, 1] (b) Use the Gram-Schmidt process to find an orthonormal basis for P2(R) with re- spect to this inner product (c) Find a polynomial q(x) such that for every p E P2R
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space...
4) Consider the inner product space P2(R), with inner product 0 (a) Use the Gram-Schmidt process...
4) Consider the inner product space P2(R), with inner product 0 (a) Use the Gram-Schmidt process to construct an orthonormal basis from the basis (b) Using your answer to part (a), give the least squares approximation in P2(R) to the function f(x)on the interval [0, 1 (Hint: You may use the following result without proof: oe d(an!)where a 1, anor n1,2....) ane- n!), where do -I, ln
[A] Consider the inner product space obtained by equipping ?[0,2] with the inner product given below:...
[A] Consider the inner product space obtained by equipping ?[0,2] with the inner product given below: 〈?(?),?(?)〉 = ∫ ?(?)?(?)?? 2 0 Determine the value of each of the following (simplifying where possible; no decimals). You do not have to show the steps of calculating the integrals, but must at least write the integrals used in your calculations. (A.1) 〈?,1〉 (A.2) ‖ ? − 1 ‖ (A.3) ?(??,?? + 10), i.e. the distance between ?? and ?? +...
Problem 1. Let the inner product (,) be defined by (u.v)xu (x)v (x) dx, and let the norm Iilbe de...
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,...
4. (6pt) Use the inner product (f,g)f ds to determine the following. (a) Determine if the functio...
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...
1: 1 131 2 Given matrix A 2 2 2. matrix P and I S set 2. a) Show that matrix P diaqonalizes A and find D(diagonal m...
1: 1 131 2 Given matrix A 2 2 2. matrix P and I S set 2. a) Show that matrix P diaqonalizes A and find D(diagonal matnx) that matches. 6) Find the eigen values of A Observe that the columns of P form set S c) orthogonal Set using the inner product standard show that set S is not an Use the Gram- Schmidt process to get an orthonormal set from S using inner product standard
1: 1 131...
A] Consider the inner product space obtained by equipping ?[0,2] with the inner product given below:...
A] Consider the inner product space obtained by equipping ?[0,2] with the inner product given below: 〈?(?),?(?)〉 = ∫ ?(?)?(?)?? 2 0 Determine the value of each of the following (simplifying where possible; no decimals). You do not have to show the steps of calculating the integrals, but must at least write the integrals used in your calculations. (A.3) ?(??,?? + 10), i.e. the distance between ?? and ?? + 10 . (A.4) Determine the value of ?...
4) Consider the inner product space P2(R), with inner product (a) Use the Gram-Schmidt process to construct an orthonormal basis from the basis (b) Using your answer to part (a), give the least squares approximation in P2(R) to the function f(x)on the interval [0, 1. Hint: You may use the following result without proof f Ine* dr = (-1)"(ane-n!), where ao = 1, an- | n. + | , for n-1, 2, ).
4) Consider the inner product space P2(R),...
Use the Gram-Schmidt process to transform the basis, B = {(1,2), (3, 4)} for R² into (a) an orthogonal basis for R and (b) an orthonormal basis for R using the Euclidean inner product; that is, dot product, and use vectors in the order in which they are given.
(4) Consider the inner product space P2(R), with inner product (a) Use the Gram-Schmidt process to construct an orthonormal basis from the basis 11, r, r2) b) Using your answer to part (a), give the least squares approximation in P2(R) to the function f(x) e on the interval [0, Hint: You may use the following result without proof: J İlne dra(-1)"(ane-n!), where ao-1, an-le! + îl , for n-1, 2, or n=1,2 .. ).
(4) Consider the inner product space...
NEED (B) AND (C)
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of continuous real-valued funo- tions on the domain [-1, 1] (b) Use the Gram-Schmidt process to find an orthonormal basis for P2(R) with re- spect to this inner product (c) Find a polynomial q(x) such that for every p E P2R
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space...
4) Consider the inner product space P2(R), with inner product 0 (a) Use the Gram-Schmidt process to construct an orthonormal basis from the basis (b) Using your answer to part (a), give the least squares approximation in P2(R) to the function f(x)on the interval [0, 1 (Hint: You may use the following result without proof: oe d(an!)where a 1, anor n1,2....) ane- n!), where do -I, ln
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,...
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...
1: 1 131 2 Given matrix A 2 2 2. matrix P and I S set 2. a) Show that matrix P diaqonalizes A and find D(diagonal matnx) that matches. 6) Find the eigen values of A Observe that the columns of P form set S c) orthogonal Set using the inner product standard show that set S is not an Use the Gram- Schmidt process to get an orthonormal set from S using inner product standard
1: 1 131...
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