Let p(x) = a, +a,x+ a,x* +a,x' and g(x) = 6, + 6x+ 6,x + b,x' be vectors inP, with the standard inner product space on P,defined by< p(x).q(x) >= a,b, + a,b, + a,b, + a,b;.a) Find the distance between fand g f - | angle of f(x) and h(x)b) Use the Gram-Schmidt process to form an orthogonal set for the functionsf(x) = 1-x-x* + 2x', g(x) = -2+ 2x - x and h(x) = x - x* + 2x

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Let p(x) = a, + a,x+ a,x' + a,x' and q(x) = 6, + ,x+5,x + b,x' be vectors in P, with the standard inner product space on P, defined by %3D < p(x).q(x) >= a,b, + a,b, + a,b, + a,b;. a) Find the distance between fand g f- g. angle of f(x) and h(x) b) Use the Gram-Schmidt process to form an orthogonal set for the functions f(x) = 1-x- x + 2x', g(x) =-2+ 2x - x' and h(x) = x - x + 2x

Let p(x) = a, + a,x+ a,x' + a,x' and q(x) = 6, + ,x+5,x + b,x' be vectors in P, with the standard inner product space on P, defined by %3D < p(x).q(x) >= a,b, + a,b, + a,b, + a,b;. a) Find the distance between fand g f- g. angle of f(x) and h(x) b) Use the Gram-Schmidt process to form an orthogonal set for the functions f(x) = 1-x- x + 2x', g(x) =-2+ 2x - x' and h(x) = x - x + 2x

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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Question

Let p(x) = a, +a,x+ a,x* +a,x' and g(x) = 6, + 6x+ 6,x + b,x' be vectors in
P, with the standard inner product space on P,defined by
< p(x).q(x) >= a,b, + a,b, + a,b, + a,b;.
a) Find the distance between fand g f - | angle of f(x) and h(x)
b) Use the Gram-Schmidt process to form an orthogonal set for the functions
f(x) = 1-x-x* + 2x', g(x) = -2+ 2x - x and h(x) = x - x* + 2x

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