Finding an orthogonal basis using the Gram-Schmidt process. Let {u₁(x) = -3, u₂(x) = 18x, u(x) = -8x²} be a basis for a subspace of P₂. Use the Gram-Schmidtprocess to find an orthogonal basis under the integration inner product (ƒ,9) = f(a)(w) da on C[0, 1].Orthogonal basis: {u₁(x) = -3, v₂(x) = 18x + a, vs(x) = -8c²+bx+c}a = Ex: 1.23b = Ex: 1.23c = Ex: 1.23

Given: It is given that u1x=-3, u2x=18x, u3x=-8x2 is a basis for a subspace of P2. Also, given that…

Answered: Let {u₁(x) = -3, u₂(x) = 18x, uz (x) =…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

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Let fi = 1+a + 5r², f2 = 1+ 2x + 8r². B = (f1, f2) is a basis for the subspace V = {ao+a,x+ aza² : 2a0 + 3a1 – az = 0} of R2[r]. () Let g = -3+4r + 6x². If [g]B then s = %3D a) 10 b) 3 c) -3 d) -10 e) vector g is not in V.
Let {u₁ (x) = 12, u₂(x) = − 18x, uz (x) = 8x²} be a basis for a subspace of P2. Use the Gram-Schmidt 1 process to find an orthogonal basis under the integration inner product (f, 9) = " f(a)g(2) da on C[0, 1]. orthogonal basis: {v₁ (x) = 12, v₂ (x) = − 18x + a, v³(x) = 8x² + bx+c} a = Ex: 1.23 = Ex: 1.23 c = Ex: 1.23
I know the basis converted to orthogonal is {<2, 1, -1, 1>,<11, -12, 5, -5>,<-1, -3, 0, 5>} and that the magnitude of these will be sqrt(7), sqrt(315), sqrt(35) - but I'm not sure how to use these to convert the basis to orthonormal.

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