Question and Answers Forum
OthersQuestion and Answers: Page 13
|
Question and Answers Forum |
|
OthersQuestion and Answers: Page 13 |
|
|
| 1) Compute in S_a , a^(−1) ba where a=(1 2)(1 3 5), b=(1 5 7 1) 2) Given permutation α = (1 2)(3 4), β = (1 3)(5 6). Find a permutation x∈S_6 ∃αx = β. help! |
| 1) Find the sign of odd or even (or pality) of permutation θ=(1 2 3 4 5 6 7 8) 2) prove that any permutation θ:S→S where S is a finite set can be written as a product of disjoint cycle help! |
| Prove that the order of any permuta− tion θ is the least common multiple of the length of its disjoint cycles. hi |
| Express as the product of disjoint cycle the permutation a) θ(1)=4 θ(2)=6 θ(1)=5 θ(4)=1 θ(5)=3 θ(6)=2 b) (1 6 3)(1 3 5 7)(6 7)(1 2 3 4 5) c) (1 2 3 4 5)(6 7)(1 3 5 7) Find the order of each of them help! |
|
|
|
|
|
|
| Determine whether f(x)=(1/x)(2x^2 +1)is: 1.A function 2. injective 3. surjective 4. bijective |
|
|
| if x,y,z are three distinct complex numbers such that (x/(y−z))+(y/(z−x))+(z/(x−y)) = 0 then find the value of Σ (x^2 /((y−z)^2 )) |
| show that f(x,y) = {_(0 (x,y)=(0,0)) ^(((x^2 y)/(x^6 + 2y^2 )) (x,y)≠ (0,0)) has a directional derivative in the direction of an arbitrary unit vector φ at (0,0), but f is not continous at (0,0) |
| prove that ∣a+(√(a^2 −b^2 ))∣ + ∣a − (√(a^2 −b^2 ))∣ = ∣a+b∣ +∣a−b∣ a,b ∈ C |
| Prove a non−empty set S of a group G wrt binary operation ∗ is a sub− group of G. Iff 1) a,b ∈ S ⇒ a∗b∈S 2) a ∈ S ⇒ a^(−1) ∈ S. Hello |
| Prove that the order of a subgroup S of a finite group G, always divide the order of group G. |
| Let H be a non−empty subset of a group G, prove that the follow− ing are equivalent 1) H is a subgroup of G 2) for a,b ∈ H, ab^(−1) ∈ H 3) for a,b ∈ ab ∈ H 4) for a ∈ H, a^(−1) ∈ H Hint: prove 1)→2)→3)→4)→1) Help!!! |
| Show that C={−1,1,−ı,ı} where ı=(√(−1)) with addition operation is a group. Help! |
| Ques. 1 Let (G,∗) be a group, then show that for each a∈G, ∃ a unique element e∈G ∣ a∗e=e∗a=a Ques. 2 If a∈G ⇒ x∈G and x is unique show that if x∗a=e, then a∗x=e. Hello! |
| Check whether (Q, ∙) is a group or not Hello bosses! |
|
|
| Ques. 2 (Metric Space Question) Let d be a metric on a non−empty set X. Show that the function U is defined by U(x,y)=((d(x,y))/(1+d(x,y))), where x and y are arbitrary element X is also a metric on X. |
| Ques. 1 (Metric Space Question) Let X = ρ_∞ be the set of all bounded sequences of complex numbers. That is every element of ρ_∞ is a complex sequence x^− ={x^− }_(k=1) ^∞ such ∣x_i ∣<Kx^− , i=1,2,3,... where Kx is a real number which may define on x for an arbitrary x^− ={x_i }_(i=1) ^∞ and y^− ={y_i }_(i=1) ^∞ in ρ_∞ we define as d_∞ (x,y)=Sup∣x_i −y_i ∣, Verify that d_∞ is a metric on ρ_(∞.) |
| Divide a 113mm line into ratio 1:2:4 |
|
|
| Σ_(n=1) ^∞ (((−1)^n (x+1)^n )/((n+1)ln(n+1))) |
| x + ln(1−x) = 0.1614, find x?1II I think we can use Lambert BOSSES, help your boy! |