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Use the polynomial inner product to find the projection of f(x) onto g(x). (a) f(x) =...
Please attempt all questions. 2. Use the polynomial inner product to find the projection of 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)....
Use the continuous function on the interval [0, 1] inner product to find the projection of...
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) = -x2 – 1, g(x) = x2 (b) f(x) = 2x2, g(x) = x + 1 (c) f(x) = -x – 1, g(x) = x2 + 3
(3 points) The function (f, g) = f(-2x(-2) + f(0)g(0) + f(2)g(2) defines an inner product...
(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.
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...
(1 point) Use the inner product 1 0 <fig >= f(x)g(x)dx in the vector space Cº[0,...
(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 attempt both questions 3. Use the continuous function on the interval (0,1) inner product to...
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 provide step by step solution Thank you (1 point) Use the inner product (5,8) =...
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) =
Section 5.4 Inner Product Spaces: Problem 6 Previous Problem Problem List Next Problem (1 point) Use...
Section 5.4 Inner Product Spaces: Problem 6 Previous Problem Problem List Next Problem (1 point) Use the inner product < p, q >= P(-2)(-2) + p(0)q(0) + p(3)q(3) in Pz to find the orthogonal projection of p(x) = 2x2 + 3x – 5 onto the line L spanned by g(x) = 2x2 - 4x +6. projz (p) =
(1 point) Use the inner product <p.q >= P(-3)(-3) + p(0)q(0) + p(2)q(2) in Pg to...
(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) =
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2....
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2. Hint: What is the matrix of the projection onto the coordinate axis x1? Problem 5. Problem 5.4 on page 23. The following method is suggested: (1) Find an angle o such that the line x1 = –2x2 is obtained by rotating the x-axis by 0. (2) Convince yourself with geometry that to project a vector v onto the line x1 = –2x2 is the...
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)....
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) = -x2 – 1, g(x) = x2 (b) f(x) = 2x2, g(x) = x + 1 (c) f(x) = -x – 1, g(x) = x2 + 3
(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.
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...
(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 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 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) =
Section 5.4 Inner Product Spaces: Problem 6 Previous Problem Problem List Next Problem (1 point) Use the inner product < p, q >= P(-2)(-2) + p(0)q(0) + p(3)q(3) in Pz to find the orthogonal projection of p(x) = 2x2 + 3x – 5 onto the line L spanned by g(x) = 2x2 - 4x +6. projz (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) =
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2. Hint: What is the matrix of the projection onto the coordinate axis x1? Problem 5. Problem 5.4 on page 23. The following method is suggested: (1) Find an angle o such that the line x1 = –2x2 is obtained by rotating the x-axis by 0. (2) Convince yourself with geometry that to project a vector v onto the line x1 = –2x2 is the...
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