1. Let L: R2-R2 be defined by L(x.y) (x +2y, 2x - y). Let S be the natural basis of R2 and let T = {(-1,2), (2,0)) be another basis for R2 . Find the matrix representing L with respect to a) S b) S and1T c) T and S d) T e) Find the transition matrix Ps- from T basis to S basis. f) Find the transition matrix Qre-s from S-basis to T-basis. g) Verify Q is inverse of...
please answer all questions im out of questions to post. thats why i squeezed them in. 6. Let u = (0, -3,11) and v = (1, -5,0). (a) Find the distance between i and V. That is, find ||ū - v1|| (b) Find the angle between i and 0. (c) Find Proje(). (d) Find Projet) (e) Find i x i and show it is orthogonal to both u and . 6 For -~- al 7. (a) Let A -12 5-2...
3. Let T (V), and B be an orthonormal basis, so that M(T,B) (5+20 pts) Is T self-adjoint? Why/Why Not? (5+20 pts) Is T normal? Why/Why Not? . (10 pts/box with explanation) Now, let R E L(V) be a self-adjoint operator, SEL(V) a normal operator, and U E L(V) an operator that is neither self-adjoint nor normal; what properties do these operators have-mark R (if true only for F = R) / C (if true only for F = C)...
Explain why S is not a basis for M2,2 s-1 1 S is linearly dependent S does not span M2,2 S is linearly dependent and does not span M2,2 Explain why S is not a basis for M2,2 s-1 1 S is linearly dependent S does not span M2,2 S is linearly dependent and does not span M2,2
Prove the following: (a) Let V be a vector space of dimension 3 and let {v,U2,U3} be a basis for V. Show that u2, u2 -2+s and uvi also form a basis for V (b) Show that1-,1-2,1-- 2 is a basis for P2[r], the set of all degree 2 or less polynomial functions. (c) Show that if A is invertible, then det A (Note: Show it for any det A-1 square matrix, showing it for a 2 x 2 matrix...
Exercise 4.10.47 Consider the set of vectors S given by S -{I 4u+v-5w 12u+6 - 6 4u+4v+4w : U, V, W ER Is S a subspace of R3? If so, explain why, give a basis for the subspace and find its dimension.
1. Find a matrix A such that L(x) = A ∗ x for all x ∈ R³ .What is the relation between A and the matrix representation eLe of L with respect to the standard bases for R³and R∧4? 2. 3. Compute the matrix representative eLS of . Let L : R3 → R4 be the linear transformation given by L 22 23 [(3x1 – 2x2 – 7x3)] (5x1 – 3x3) (4x2 – 3x3) [(6x1 + 2x2 – 3x3) Let...
Please argument all your answers and explain why of your arguments so i can understand better and do not use advanced things im just taking linear algebra course. Let V be a vector space of finite dimension over a field K. T a linear operator over V and a eigenvector of T associated to the eigenvalue . If , show that . Being A any matrix associated to T in some basis of V. We were unable to transcribe this...
detail steps please 1· Let L:R'→R' bedefined by L(x,y)-(x-2y,x+2y Let S- (1.-1).(0.D)be a basis for R' and let T be the natural basis for IR2 Find the matrix representing L w. r to a) S b) Sand T c T andS d) T e) Compute L(2,-1) using the definition of L and also using the matrices obtained in a), b), c)and d)
Erin has a $100,000 basis in the stock of an S corporation. Which of the following items, if any, would not decrease her basis in the stock? a. Distributions by the S corporation that are a return of capital. b. Any expense of the S corporation that is not deductible in figuring its income and not properly chargeable to the capital account. c. All loss and deduction items of the S corporation that are separately stated and passed through to...