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On the space P₂ we define the scalar product (ao + a₁x + a₂x² | bo + b₁x + b₂x²) = 4aobo + aob₁ + a₁bo + 5a₁b₁ + 2a₂b₂. Which of the following is the (symmetric, positive definite) matrix of this scalar product, with respect to the standard basis in P₂? (Remember that the standard basis is b = (1 x x²).) (Note, only 1 answer.) 4 20 0 50 0 02 4 01 0 50 1 02 4 1 0 1 0 50 02 3 1 0 1 5 1 0 1 3

On the space P₂ we define the scalar product (ao + a₁x + a₂x² | bo + b₁x + b₂x²) = 4aobo + aob₁ + a₁bo + 5a₁b₁ + 2a₂b₂. Which of the following is the (symmetric, positive definite) matrix of this scalar product, with respect to the standard basis in P₂? (Remember that the standard basis is b = (1 x x²).) (Note, only 1 answer.) 4 20 0 50 0 02 4 01 0 50 1 02 4 1 0 1 0 50 02 3 1 0 1 5 1 0 1 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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On the space P₂ we define the scalar product (ao + a₁x + a₂x² | bo + b₁x + b₂x²) = 4aobo + aob₁ + a₁bo + 5a₁b₁ + 2a₂b₂. Which of the following is the (symmetric, positive definite) matrix of this scalar product, with respect to the standard basis in P₂? (Remember that the standard basis is b = (1 x x²).) (Note, only 1 answer.) 4 20 0 50 0 02 4 01 0 50 1 02 4 1 0 1 0 50 02 3 1 0 1 5 1 0 1 3
Transcribed Image Text:On the space P₂ we define the scalar product (ao + a₁x + a₂x² | bo + b₁x + b₂x²) = 4aobo + aob₁ + a₁bo + 5a₁b₁ + 2a₂b₂. Which of the following is the (symmetric, positive definite) matrix of this scalar product, with respect to the standard basis in P₂? (Remember that the standard basis is b = (1 x x²).) (Note, only 1 answer.) 4 20 0 50 0 02 4 01 0 50 1 02 4 1 0 1 0 50 02 3 1 0 1 5 1 0 1 3
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