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**princess snowwhite**- Replies: 1

give an example of an infinite group having all elements of finite order.

thanks to you all

**princess snowwhite**- Replies: 1

Which of the following statements is false?

a>any abelian group of order 27 is cyclic

b>any abelian group of order 14 is cyclic

c>any abelian group of order 21 is cyclic

d>any abelian group of order 30 is cyclic

I am using multiplication.

does anyone know how to solve it?

**princess snowwhite**- Replies: 12

let G be a group of order p^2 where p is a prime no. let x belongs to G. prove that {y belongs to G: xy=yx}=G

welcome

I needed the definition and example also

I don't know what is this eigen pair, THAT'S WHY i am asking you

**princess snowwhite**- Replies: 10

Can anyone tell me how to solve a problem using c program by "eigen pair by power method"?

so I . the set should be infininte

yes for n=2, [n]=2 but when n=1.6, [n]=1

I think the set will be infinite. does anyone has anything else in mind?

Yes It Does Mean That Each Roq Sums To 1

**princess snowwhite**- Replies: 6

f(x)= [x] + (x-[x])^2.

where [x] means largest integer not exceeding x.

then find set of all values taken by f

**princess snowwhite**- Replies: 8

let P be any n*n square matrix whose row sum equals 1 then for any postive m the row sum of the matrix P^m equals 1 ,state true or false

Thank you all .

Ops! Sorry........ Yes I wanted T2(v)= −v

I have no idea about the answer. But the question is correct.

**princess snowwhite**- Replies: 6

hi! I joined this forum few days ago and it seems to be pretty good. Well I am a student currently pursuing higher studies in mathematics. I am here to learn and get some help when I am confused. Nice to meet you all.

**princess snowwhite**- Replies: 0

let v1 and v2 be non zero vectors in R^n , n>=3, such that v2 is not a scalar multiple of v1, prove that there exists a linear transformation T:R^n-->R^n such that T^3=T, Tv1=v2 and T has at least three distinct eigen values

**princess snowwhite**- Replies: 1

let T:R^n-->R^n be a LT where n>-2 and for k<=n,

let E={v1,v2,....,vk} and F={Tv1,Tv2,.....,Tvk}.

then

a>if E is LI then F is LI

b>if F is LI then E is LI

c>if F is LI then E is LD

d>if E is LI then F is LD

here i think the answer will be b.

let F be LI and E be LD. then c1v1+....+civi+....+ckvk= 0 where ci not equals to zero. then T( c1v1+....+civi+....+ckvk)= T(0)=0

or c1Tv1+...+ciTvi+....+ckTvk=0 where ci is non zero wich contradicts that F is LI, hence E must be LI

JUST TELL ME IF THERE IS ANYTHING WRONG IN THIS PROOF

**princess snowwhite**- Replies: 1

let V be a vector space of all polynomials with real coefficients with degree at most n where n>=2, consider the elements of V as a function from R to R. define W={p belongs to V∫egration 0 to 1 p(x) dx=0} , show thar W is a subspace of V and dim W= n.

I have proved that W is a subspace but couldnot prove that din W= n

**princess snowwhite**- Replies: 4

let V be a real n-dimensional vector space and let T:V-->V be a LT saisfying T(v)= - v for all v belongs to V.

1. show n is even

2.use T to make V into a cmplex vector space such that the multiplication by complex numbers extends the multiplications by real numbers

3. show that with respect to complex vector space structure on V obtained in 2. , T is a complex linear transformation