Let A = [ 1 1 0 1] ∈ GL(2, R). Compute the centralizer of A. Is the centralizer abelian? Explain.
1 (5 points) Let A E GL(2, R). Compute the centralizer of A. Is the centralizer abelian? Explain. (61) =
Find the centralizer of A in GL(2, R); in SL(2, R); in O(2, R).
Definition. Let G be a group and let a € G. The centralizer of a is C(a) = {9 € G ag = ga}, i.e. it consists of all elements in G that commute with a. (18) (a) In the group Zui, find C(3). (b) Complete and prove the following: If G is an Abelian group and a EG, then C(a) = _. (c) Prove or disprove: In every group G, there exists a E G such that C(a) =...
1- (2,5+2,5 mark) Consider in GL(2, Q), the subset (a=1 or a=-1),bez Prove that H, with multiplication, is a subgroup of GL(2,Q) a) Is the function b) an homomorphism of groups? Justify your answer 2 (3 marks) Let G be a group and a E G an element of order 12. Find the orders of each of the elements of (a) 3- (1+1,5 marks) Let G be a group such that any non-identity element has order 2. Prove that a)...
1 0 0 0 0 I. (2 points each item) Let R=13 0 1 0 0 (a) Let A be any other matrix with 5 rows. Explain in words what multiplying A on the left by R does to the rows of A (b) Explain in words what you would do to undo the effect of multiplying A on the left by R (c) Without doing any computations, write down the inverse of R (d) Note that (RTA)T-AT((RT)T-ATR. Let C...
GL(2, Z3) = {[a ] a, b,c,d € Zz, ad – bc = 0} What is the centralizer for at least three different elements in your group.
1. -12 points PooleLinAlg4 3.1.004. 0/3 Submissions Used Let r 2 5 2 -3 1 Compute the indicated matrix. (If this is not possible, enter DNE in any single blank). Need Help? ReaditTalk to a Tuter Submit Answer Save Progress Practice Another Version
1 1 1 0 -5 0 -77 0 2. 0 2 2. Let A be a 4 x 5 matrix whose reduced row echelon form is R 0 0 0 3 LO 0 0 0 0 For parts (b) and (c), write the solution in parametric vector form. (a) (2 points) Is the equation Ax b consistent for all b in R4? Why or why not? (b) (4 points) Solve the equation Ax = 0. 4 -3 -3 (c) (3...
2 (2+2+1 marks) Consider the function GL(2,R-R A det A a) Prove that f is a surjective homomorphism. b) Verify that N-AL()dAE Ois a nomal subgroup of GL(2.R) GL(2.Ra group? a group? If so, with what operation? c) Is
2 (2+2+1 marks) Consider the function GL(2,R-R A det A a) Prove that f is a surjective homomorphism. b) Verify that N-AL()dAE Ois a nomal subgroup of GL(2.R) GL(2.Ra group? a group? If so, with what operation? c) Is
Complex Analysis
1. Let γ is a positively oriented circle centered at the origin with radius r r > 0 ecos(e2) +21)9 (a) For r £ {1,2}, compute the integral .Дег+1)(2+2)3 d (b) For r and 2, find the principal value of that integral, if it exists.
1. Let γ is a positively oriented circle centered at the origin with radius r r > 0 ecos(e2) +21)9 (a) For r £ {1,2}, compute the integral .Дег+1)(2+2)3 d (b) For r...