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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 44E

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