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Let {u₁(x) = -3, u₂(x) = − 18x, uz (x) = -8x²} be a basis for a subspace of P2. Use the Gram- Schmidt process to find an orthogonal basis under the integration inner product (f, g) = [ f(x)g(x) da on C[0, 1]. Orthogonal basis: {v₁(x) = −3, v₂ (x) = −18x + a, v³ (x) = − 8x² +bx+c}

Let {u₁(x) = -3, u₂(x) = − 18x, uz (x) = -8x²} be a basis for a subspace of P2. Use the Gram- Schmidt process to find an orthogonal basis under the integration inner product (f, g) = [ f(x)g(x) da on C[0, 1]. Orthogonal basis: {v₁(x) = −3, v₂ (x) = −18x + a, v³ (x) = − 8x² +bx+c}

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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Hi, can I please have some help with this problem? The steps to solve it are unclear to me. Thanks in advance!

Let {u₁(x) = −3, u2 (x) = −18x, uz (x) = − 8x²} be a basis for a subspace of P2. Use the Gram- Schmidt process to find an orthogonal basis under the integration inner product (f, g) = f* f(x)g(x) da on C[0, 1]. Orthogonal basis: {v₁(x) = −3, v₂ (x) a Ex: 1.23 b = Ex: 1.23 = −18x + a, v3 (x) = −8x² +bx+c} c = Ex: 1.23
Transcribed Image Text:Let {u₁(x) = −3, u2 (x) = −18x, uz (x) = − 8x²} be a basis for a subspace of P2. Use the Gram- Schmidt process to find an orthogonal basis under the integration inner product (f, g) = f* f(x)g(x) da on C[0, 1]. Orthogonal basis: {v₁(x) = −3, v₂ (x) a Ex: 1.23 b = Ex: 1.23 = −18x + a, v3 (x) = −8x² +bx+c} c = Ex: 1.23
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