Math Is Fun Forum

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

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

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

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

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.

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

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