Give an example of a vector space which has 125 elements

Question

Give an example of a vector space which has 125 elements. I don't know how proceed!!! Is there any technique about the field??

Before posting, have look here at this site, e.g., here. – Dietrich Burde Jan 20 '18 at 14:38 — Dietrich Burde, Jan 20 '18 at 14:38

score 4 · Accepted Answer · answered Jan 20 '18 at 14:37

4

Just consider the field $\mathbb Z_5$ and mutiply it $3$ times with itself. Then new set over the field $\mathbb Z_5$ is a vector space with $125$ elements.

answered Jan 20 '18 at 14:37

GhD

926

cansomeonehelpmeout · Answer 2 · 2018-01-20T14:46:59.253

1

$\frac{\mathbb{Z}_5[x]}{(x^3)}$ as a $\mathbb{Z}_5$-module, which is $\{a+bx+cx^2\mid a,b,c\in\mathbb{Z}_5\}$.

This is the same as $$V=\left < [a,b,c]\mid a,b,c\in\mathbb{Z}_5\right>$$

which have $5^3=125$ elements.

edited Jan 20 '18 at 14:46

answered Jan 20 '18 at 14:40

cansomeonehelpmeout

12,782
3
22
49

Give an example of a vector space which has 125 elements

2 Answers2