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1. Let V = P₂(x) and define < f,g >= 2f (0)g(0) + f(1)g(1) +3f (2)g(2). (a) Prove that this is an inner product (You may use the fact that a quadratic poly- nomial with three roots must be zero).

1. Let V = P₂(x) and define < f,g >= 2f (0)g(0) + f(1)g(1) +3f (2)g(2). (a) Prove that this is an inner product (You may use the fact that a quadratic poly- nomial with three roots must be zero).

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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1. Let V = P₂(x) and define < f,g>= 2ƒ(0)g(0) + f(1)g(1) +3ƒ(2)g(2). (a) Prove that this is an inner product (You may use the fact that a quadratic poly- nomial with three roots must be zero). (b) Let f(x) = 1 + x and g(x) orthogonal to f. = x² - 3. Compute Projƒg and the projection of g
Transcribed Image Text:1. Let V = P₂(x) and define < f,g>= 2ƒ(0)g(0) + f(1)g(1) +3ƒ(2)g(2). (a) Prove that this is an inner product (You may use the fact that a quadratic poly- nomial with three roots must be zero). (b) Let f(x) = 1 + x and g(x) orthogonal to f. = x² - 3. Compute Projƒg and the projection of g
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