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Use the continuous function on the interval [0, 1] inner product to find the projection of...
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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...
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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 polynomial inner product to find the projection of f(x) onto g(x). (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.
5. (15') Define the inner-product on C([-1,1]), the space of all continuous functions on the interval [-1,1], by (f(a), g(x) = $ $(a)g(x) dr. (a) Use Gram-Schmidt algorithm to convert the set {1,1 + ,(1+x)?} to an orthogonal set. (b) Is the set you found in Part (a) still orthogonal if the interval of integral in the definition of inner-product is changed to [0, 1]? Explain your an answer.
interval-1,1. If f.geCL1.], we'l 7) The field of play is Cil the space of all functions that are continuous on the define the inner product as (f,g)= f'f(x)g(x)dx. The question is simply this: Find the orthogonal projection of e" onto P, and graph both functions on [-2,2].
interval-1,1. If f.geCL1.], we'l 7) The field of play is Cil the space of all functions that are continuous on the define the inner product as (f,g)= f'f(x)g(x)dx. The question is simply this:...
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(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) =
5. (15') Define the inner-product on C([-1,1]), the space of all continuous functions on the interval [-1, 1), by (5(2), gla) - s(z)g(z) dr. (a) Use Gram-Schmidt algorithm to convert the set (1,1 + 1,(1 + x)2} to an orthogonal set. (b) Is the set you found in Part (a) still orthogonal if the interval of integral in the definition of inner-product is changed to [0, 1]? Explain your answer.
(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) =
(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) =