V = {S:(-1,1] +R1 f(a)d f(x)dx = 0} Prove that the space described above with the...

Question

Question

V = {S:(-1,1] +R1 f(a)d f(x)dx = 0} Prove that the space described above with the natural addition and scalar multiplication

math algebra

Answer 1

Answer #1

a Let fog Ev f(x) da = 0 and Soor de g(a) da = 0 then If+g)(x) = f(x) + 9(2) So Sf+8) (2) d [ f(x) +964)] d8 f(a)da + g(x2 da

Answer 2

Similar Homework Help Questions

2. On subspaces of C(-1,1) Let V C(-1,1) be the vector space of all continuous real...

2. On subspaces of C(-1,1) Let V C(-1,1) be the vector space of all continuous real valued functions on on the interval (-1, 1), with usual addition and scalar multiplication. (a) Verify, if the set W-f eV: f(0)-0is a subspace of V or not? (b) Verify, if the set W-Uev f(0) 1 is a subspace of V or not? (c) Verify, if the set W-İfEV:f(x)-0V-2-z is a subspace of V or not? 1b) PrtScn Home FS F6 F7 F8 5
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of co...

NEED (B) AND (C) 2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of continuous real-valued funo- tions on the domain [-1, 1] (b) Use the Gram-Schmidt process to find an orthonormal basis for P2(R) with re- spect to this inner product (c) Find a polynomial q(x) such that for every p E P2R 2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space...
. Let V be a vector space and S a set. Let V$ = {f S...

. Let V be a vector space and S a set. Let V$ = {f S V} on VS by be the set of all functions from S to V. Define addition and scalar multiplication (fg)(s) f(s) + g(s) and (af)(s) = af(s) for all a F, f,gE V, and s E S. Show that VS is a vector space

just part c,d, and e please!! Let V be a finite-dimensional vector space over F. For...

just part c,d, and e please!! Let V be a finite-dimensional vector space over F. For every subset SCV, define Sº = {f eV" f(s) = 0 Vs ES}. (a) Prove that sº is a subspace of V* (S may not be a subspace!) (b) If W is a subspace of V and r & W, prove that there exists an few with f(x) +0. (c) If v inV, define u:V* → F by 0(f) = f(v). (This is linear...
Let S = {x ER:[x]<1}=(-1,1). We will refer to E as hyperbolic relativity space. Now a+b...

Let S = {x ER:[x]<1}=(-1,1). We will refer to E as hyperbolic relativity space. Now a+b define a binary operation by: if a,beR and ab +-1, then aob= 1+ ab Proposition 1. (5,0) is a group. Remark. This is the kind of problem that every student should become competent at doing. Perhaps some of the details here are more challenging than normally but understanding what are the steps to follow in such a problem is basic, and everyone should understand...
Let V = M2x2 be the vector space of 2 x 2 matrices with real number...

Let V = M2x2 be the vector space of 2 x 2 matrices with real number entries, usual addition and scalar multiplication. Which of the following subsets form a subspace of V? The subset of upper triangular matrices. The subset of all matrices 0b The subset of invertible matrices. The subset of symmetric matrices. Question 6 The set S = {V1, V2,v;} where vi = (-1,1,1), v2 = (1,-1,1), V3 = (1,1,-1) is a basis for R3. The vector w...

6. (i) Prove that if V is a vector space over a field F and E...

6. (i) Prove that if V is a vector space over a field F and E is a subfield of F then V is a vector space over E with the scalar multiplication on V restricted to scalars from E. (ii) Denote by N, the set of all positive integers, i.e., N= {1, 2, 3, ...}. Prove that span of vectors N in the vector space S over the field R from problem 4, which we denote by spanr N,...
please help me,thanks! 3. Let Fo be a field with 9 elements. Consider the set S () e Fo] deg(f()) 18, f( f(1) (2)) (4) 0 and (a) Compute IS. (b) Prove that S is a vector space over F (c) Compute...

please help me,thanks! 3. Let Fo be a field with 9 elements. Consider the set S () e Fo] deg(f()) 18, f( f(1) (2)) (4) 0 and (a) Compute IS. (b) Prove that S is a vector space over F (c) Compute dimF, S Let V be a vector space over F. Prove that X C V is a subspace if and only if v, w E X implies av+wEX for every aEF 3. Let Fo be a field with...
(1 point) Use the inner product 1 0 <fig >= f(x)g(x)dx in the vector space Cº[0,...

(1 point) Use the inner product 1 0 <fig >= f(x)g(x)dx in the vector space Cº[0, 1] to find the orthogonal projection of f(x) = 6x2 + 1 onto the subspace V spanned by g(x) = x – į and h(x) = 1. projy(f) =

Let V be a finite-dimensional vector space over F. For every subset SCV, define Sº =...

Let V be a finite-dimensional vector space over F. For every subset SCV, define Sº = {f EV* | f(s) = 0 Vs E S}. (a) Prove that sº is a subspace of V* (S may not be a subspace!) (b) If W is a subspace of V and x € W, prove that there exists an fe Wº with f(x) + 0. (c) If v inV, define û :V* + F by ū(f) = f(u). (This is linear and...