Find a basis {p(x), q(x)} for the vector space {f(x) e P2[x] | f' (7) = f(1)} where P2[x] is the vector space of polynomials in x withdegree at most 2.You can enter polynomials using notation e.g., 5+3xx for 5 + 3x.p(x) =q(x)

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Answered: Find a basis {p(x), q(x)} for the…

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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2. (a) Show that the polynomials p, (x)=1+x, p,(x)=1+2.x – x², p;(x)=x+x² are linearly independent. (b) Decide if polynomial q(x)=-1+x is in the span{p, (x), P2 (x), P;(x)} .
Find the least squares approximating polynomial of degree 2 on the interval [-1, 1] for the function f(x)=x²-2x +3
Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), |lp||, ||9||, and d(p, q) for the polynomials in P2. p(x) = 2x + 5x², q(x) = x - x² (a) (p, q) (b) ||P|| (c) ||9|| (d) d(p, q)
Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), ||p||, ||9||, and d(p, q) for the polynomials in P2. p(x) = 4x + 3x2, g(x) = x - x² (a) (p, q) (b) ||P|| (c) |||| d(p, q) (d)
Consider the vector space V of all the real polynomials of degree less than or equal to three, p(x) = ax^3 + b x^2 + c x + d, and consider the linear transformation T: V ------> V given by the derivative, i.e., T( p ) = p' = 3ax^2 + 2 b x + c. Find the eigenvalues and eigenvectors of this transformation.

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Find a basis {p(x), q(x)} for the vector space {f(x) e P2[x] | f' (7) = f(1)} where P2[x] is the vector space of polynomials in x with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5 + 3x. p(x) = q(x)