1: On the polynomial space P₁ John chooses the scalar product (flg)₁ = ₁f(x)g(x) dx, while Jim uses the scalar product (flg)₂ = f f(x)g(x)dx. What of the following applies? (Note, only 1 answer). A) The polynomial f(x) = x and the constant polynomial g(x) = 3 are orthogonal to each other with respect to both scalar products. B) The polynomial f(x) = x and the constant polynomial g(x) = 3 are orthogonal to each other with respect to John's scalar product, but not Jim's. C) The polynomial f(x) = x and the constant polynomial g(x) = 3 are orthogonal to each other with respect to Jim's scalar product, but not John's D) The polynomial f(x) = x and the constant polynomial g(x) = 3 are not are orthogonal to each other with respect to both scalar products.
1: On the polynomial space P₁ John chooses the scalar product (flg)₁ = ₁f(x)g(x) dx, while Jim uses the scalar product (flg)₂ = f f(x)g(x)dx. What of the following applies? (Note, only 1 answer). A) The polynomial f(x) = x and the constant polynomial g(x) = 3 are orthogonal to each other with respect to both scalar products. B) The polynomial f(x) = x and the constant polynomial g(x) = 3 are orthogonal to each other with respect to John's scalar product, but not Jim's. C) The polynomial f(x) = x and the constant polynomial g(x) = 3 are orthogonal to each other with respect to Jim's scalar product, but not John's D) The polynomial f(x) = x and the constant polynomial g(x) = 3 are not are orthogonal to each other with respect to both scalar products.
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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Transcribed Image Text:1:
On the polynomial space P₁ John chooses the scalar product (flg)₁ = ₁f(x)g(x) dx, while Jim
uses the scalar product (flg)₂ = f f(x)g(x)dx. What of the following applies? (Note, only 1
answer).
A) The polynomial f(x) = x and the constant polynomial g(x) = 3 are orthogonal to each
other with respect to both scalar products.
B) The polynomial f(x) = x and the constant polynomial g(x) = 3 are orthogonal to each
other with respect to John's scalar product, but not Jim's.
C) The polynomial f(x) = x and the constant polynomial g(x) = 3 are orthogonal to each
other with respect to Jim's scalar product, but not John's
D) The polynomial f(x) = x and the constant polynomial g(x) = 3 are not are orthogonal to
each other with respect to both scalar products.
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