20. Let V (R) be the vector space of polynomials with inner product defined by(f, g) = [f() g(1) dt for f,ge V. If f(x)=x +x – 4, g(x) =x – 1 V xe [0, 1]then find (f, g), IIf|| and || gl-21State and

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Answered: 20. Let V (R) be the vector space of…

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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6. Show all the steps clearly please
Let f (x) C = C = = x on [0, 5], and let P = {0, c, 5}. Find two values of c in (0, 5) such that Uf (P) = 22. (smaller value) (larger value)
Q 2.8 Consider the functions f₁(x)=x and f₂(x)=3-5cx on the interval of [0,1]. so that a) Find the value of the constant c f, and £₂ are orthogonal on [0, 1]. Your answer should be symbolic and should not have any decimals ) Using the value of the constant c from part(a), find the norm of f₂ on the interval '[0, 1];
7. Let V(C) be the vector space of all continuous complex valued functions on 1 [0, 1]. If f(t), g (1) e V then show that (f (t), g (t)) = [ƒ (t) g (t) dt defines an inner product on V (C).
Find the kernel and range of each of the following linear operators on P^3(the vector space of polynomials with degree less than 3):(a) L(p(x)) = xp′(x), where p′(x) is the derivative of p(x). Hint: Start with p(x) = ax2 + bx + c. (b) L(p(x)) = p(x) − p′(x).
easy functional analysis
Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies. v(3,-2) = 0 Vs(3,-2) = 5 u(3,-2) = -3 Us(3,-2) = -7 ut(3,-2) = 7 Fu(-3,0) = -9 Vt(3,-2) = -1 Fv(-3,0) = -5 Find Wę(3,-2) and We(3,-2). Ws(3,-2) = W+(3,-2) =
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20. Let V (R) be the vector space of polynomials with inner product defined by f.g) = [f() g(1) dt for f,g e V. If f(x) =x +x - 4, g(x) =x – 1 V x E [0, 1] %3D then find (f, g), ||S| and || g|l. State and