GiveanexampleofV andT:V →V,alinearmapandW ⊂V a non-trivial T -invariant subspace such that for any U such that V = W ⊕ U (a complement of W ), U is not T -invariant.?1 1? Hint Consider A = 0 1What are the eigenspaces and their complements? A Give an example of V and T: V → V, a linear map and W CVa non-trivial T-invariant subspace such that for any U such thatV = W ☺ U (a complement of W), U is not T-invariant.(61)01What are the eigenspaces and their complements?Hint Consider A-

Answered: Image /qna-images/answer/056e27a4-7e55-40a0-8a08-2e5a2e142f97.jpg

Answered: Give an example of V and T: V → V, a…

Give an example of V and T: V → V, a linear map and WC V a non-trivial T-invariant subspace such that for any U such that V=WU (a complement of W), U is not T-invariant. (1) Hint Consider A 1171 =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Also given v1 and v2 are linearly independent
Consider the operator Son the vector space by S(a+bx) = - a+b+ ( a + 2b) x A) Pick a basis B = { b₁,b₂3. Find the minimal polynomials NT, b, (X), Nr, 0₂ (x), and Ns (x) R₁ [x] given B) Show that S is cyclic by finding a vector v such that
3: Which of the following sets are closed under scalar multiplication? (1) The set of all vectors in R of the form (a, b, 9ab). (i1) The set of all polynomials a- bx+ cx in P, such that ac =D0. (iii) The set of all matrices in Mn such that A = A (A) (1) and (ii) only (B) (1) and (iii) only (C) (ii) and (iii) only (D) (1) only (E) (ii) only (F) none of them (G) (iii) only (H) all of them
Let V be a vector space with dim(V) = 3. Explain why any T: V → V has at least one real eigenvalue.
Dev
Let V be a vector space, and TV →Va linear transformation such that T(271 +372) = -201 +502 and T(371 +50₂) = 371 - 572. Then T(v₁) =₁+₂, T(₂)=₁+₂, 40₂) = ₁+ T(471
Let ₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 7x - 2x² + 2, ·(x² + 2x +2) and 3x − x² + 1. 1 a. The dimension of the subspace H is b. Is {7x − 2x² +2,- (x² + 2x +2), 3x − x² +1} a basis for ➡? choose Be sure you can explain and justify your answer. c. A basis for the subspace His { Enter a polynomial or a comma separated list of polynomials (where you can enter xx in place of x²)
Let fi = 1+2x + 3x², f2 = 2 + 3x + 4x². B = (f1, f2) is a basis for the subspace V = {ao +a1x+azx²[ao – 2a1 +a2 = 0} of R2[r]. Let g = 1+5x + 9x². If [g]g = (,) then s = a) -7 b) -5 c) 5 d) 7 e) g is not in V.
Let L: R3 R2 be defined by the following. X1 + X3 ***] 8x2 Suppose X1 L X₂ P = = 1 -(HH) 4 3 3 1 2 B₁ = 4 ={[8][;}} is an ordered basis for the domain and B₂ = is an ordered basis for the range. Find the matrix representation P for L relative to B₁ and B₂ such that [L(u)]b₂ = P[u]ß₁'