Let V be the vector space of all polynomials of degree at most 2 equipped with...
Let P2 be the real vector space of polynomials in a of degree at most 2, and let T be the real vector space of upper triangular 2 x 2 matrica b,cERThe vector space P2 is equipped with the inner product 〈p(x), q(x)-1 p(z)q(z) dr, and the vector space T is equipped with the inner product 〈A.B)=tr(AB), where tr denotes trace. Let L: P2→T be 1.p(z)dr]. Find L 0 c given by L(p(z)):-17(1) .CE :J ) 1 2 0 p(-1)...
advanced linear algebra thxxxxxxxx Consider the complex vector space P4(C) of polynomials of degree at most 4 with coeffi- cients in C, equipped with the inner product ⟨ , ⟩ defined by 5. Consider the complex vector space P4(C) of polynomials of degree at most 4 with coeffi- cients in C, equipped with the inner product (, ) defined by (f, g)fx)g(xJdx. (a) Find an orthogonal basis of the subspace Pi(C)span,x (b) Find the element of Pi (C) that is...
let P3 denote the vector space of polynomials of degree 3 or less, with an inner product defined by 14. Let Ps denote the vector space of polynomials of degree 3 or less, with an inner product defined by (p, q) Ji p(x)q(x) dr. Find an orthogo- nal basis for Ps that contains the vector 1+r. Find the norm (length) of each of your basis elements 14. Let Ps denote the vector space of polynomials of degree 3 or less,...
(1 point) Let V be the vector space P3[x] of polynomials in x with degree less than 3 and W be the subspace a. Find a nonzero polynomial p(x) in W b. Find a polynomial q(x) in V\ W. q(x)-
2. Let V be the vector space of polynomials in two variables r and y of degree at most two: V-(ar' + bry + суг + dr + ey + f | a,b,c, d, e, f E R} Let T be the linear operator on V defined by Find the Jordan canonical form of T 2. Let V be the vector space of polynomials in two variables r and y of degree at most two: V-(ar' + bry + суг...
Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 8x−5x2+3, 2x-2x2+1 and 3x2-1. a) The dimensions of the subspace H is ___________? b) Is {8x-5x2+3, 2x-2x2+1, 3x2-1} a basis for P2? ________(be sure to explain and justify answer) c) A basis for the subspace H is {_________}? enter a polynomial or comma separated list of polynomials
HW10: Problem 7 Prev Up Next (1 pt) Let V be the vector space P3z of polynomials in with degree less than 3 and W be the subspace a. Find a nonzero polynomial p(z) in w p(z) b. Find a polynomial q(z) in V\W g(z) Note: You can earn partial credit on this problem. Preview Answers Submit Answers
please help me with part a) (1 point) Let V be the vector space P3 [x] of polynomials in x with degree less than 3 and W be the subspace W - span((-4)+ 5x2,4 +5x 7x2 a. Find a nonzero polynomial pr) in W b. Find a polynomial q(x) in V\ W. qx)1-2xA2+5
7. Let V = Pa(R), the vector space of polynomials over R of degree less than 2, with inner product Define φ E p by φ(g)-g(-1) a) By direct calculation, find f e V such that (S)-dg). You are given that A 1, V3-2v) is an orthonormal basis for V (you do not need to check this). b) Find the same f as in part a, using the formula for A(6) from class. 7. Let V = Pa(R), the vector...
6. (a) Let V be a vector space over the scalars F, and let B = (01.62, ..., On) CV be a basis of V. For v € V, state the definition of the coordinate vector [v]s of v with respect to the basis B. [2 marks] (b) Let V = R$[x] = {ao + a11 + a222 + a3r | 20, 41, 42, 43 € R} the vector space of real polynomials of degree at most three. Write down...