Let {u₁(x) = 3, u₂(x) = 18x, u(x) = -8a2} 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(a)g(ar) dit on C[0, 1] 0 Orthogonal basis: {v₁(x) = 3, v₂(x) = 18x + a, vs(x) = -8x²+bx+c} a = Ex: 1.23 b= Ex: 1.23 c = Ex: 1.23

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Finding an orthogonal basis using the Gram-Schmidt process.

 

Let {u₁(x) = 3, u₂(x) = 18x, u(x) = -8a2} be a basis for a subspace of P₂. Use the Gram-Schmidt
process to find an orthogonal basis under the integration inner product (f, 9) = f(a)g(a) diet on C[0, 1].
0
Orthogonal basis: {1(x) = 3, v₂(x) = 18x + a, v₂(x) = −8x²+bx+c}
a= Ex: 1.23
b= Ex: 1.23
c = Ex: 1.23
Transcribed Image Text:Let {u₁(x) = 3, u₂(x) = 18x, u(x) = -8a2} be a basis for a subspace of P₂. Use the Gram-Schmidt process to find an orthogonal basis under the integration inner product (f, 9) = f(a)g(a) diet on C[0, 1]. 0 Orthogonal basis: {1(x) = 3, v₂(x) = 18x + a, v₂(x) = −8x²+bx+c} a= Ex: 1.23 b= Ex: 1.23 c = Ex: 1.23
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