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Perform the marquis de Laplace process on the basis {f(x) = x2 - 4x +1, g(x)...
Please attempt all 3. Perform the marquis de Laplace process on the basis {f(x) = = x2 - 4x + 1, g(x) = 2x + 4, h(x) = x2 +3} to create an orthogonal basis for the space of polynomial functions of degree < 2. 4. Use the marquis de Laplace process to show that the following set is linearly dependent: (10) 5. Use the marquis de Laplace process to show that the following set is linearly dependent: {f(x) =...
Perform the marquis de Laplace process on the basis 3 ll -1 5 to create an orthogonal basis for R3.
Please attempt both. 1. Perform the marquis de Laplace process in both possible ways (remember, you choose the lead vector) on the basis 3 -2 -1 to create an orthogonal basis for R2. Geometrically represent each process in 3 plots: The first two vectors, the projection and perpendicular, and finally the new basis. 2. Perform the marquis de Laplace process on the basis 3 -2 1 3 -1 3 5 to create an orthogonal basis for R3.
Please attempt both. 1. Perform the marquis de Laplace process in both possible ways (remember, you choose the lead vector) on the basis 3 to create an orthogonal basis for R2. Geometrically represent each process in 3 plots: The first two vectors, the projection and perpendicular, and finally the new basis. 2. Perform the marquis de Laplace process on the basis 3 -2 1 3 -1 3 5 -1 to create an orthogonal basis for R3.
Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): -1 1 ( 2 5 3 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = x2 – 3, g(x) = 4, h(x) = x2 +2} (c) In the vector space that consists of 2x2 matrices: (You'd decided what the inner product was on a previous math...
6. Determine if each basis is orthogonal. Further, is the basis orthonormal? (a) In the vector space R3 (i.e. column vectors in 3-space): 3 -1 2 3 1 5 -3 (b) In the vector space that consists of polynomial functions of degree less than or equal to 2: {f(x) = x2 – 3, 9(x) = 4, h(x) = x2 +2} (c) In the vector space that consists of 2 x 2 matrices: (You'd decided what the inner product was on...
Find the derivative of the following functions: (x2-1) f(x) = (x2 +1) f(x) = (x3 + 2x)3(4x + 5)2
Evaluate the following f(x)=x2-1 and g(x) = 3x +5. :a. f(-3) b. g(-2) c. f(0) d. g(5) 2. Find the x and y intercepts of the following functions: a) f(x) = x2 - 5x + 6 = 0b) h(x) = -2x + 20
stuck on #37 7-13 In Exercises 33 through 38. find the difference quotient, fa+ h)-a) 33. f(x)4 5x 35. f) 4x 2 34. f(x)2x 3 36. fx) x2 37. f) 38. f(x) - + 1 In Exercises 39 through 42, first obtain the composite functions f(g(x)) and g(f(x)), and then find all number r (if any) such that f(g(x)) g(f(x)). 39. fx) Vt, gt) 1 3 7-13 In Exercises 33 through 38. find the difference quotient, fa+ h)-a) 33. f(x)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...