Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm new in the University and I don't know how to solve this:

Suppose $v$ is a non null element of a vector space $V$ on $\mathbb R$. Show that the function is injection:

$\mathbb R\to V $

$t \mapsto tv$

Sorry for any misspelling.

share|cite|improve this question
up vote 1 down vote accepted

Suppose $tv = sv$, then $(t-s)v = 0$. As $v \neq 0$ (that is, it is not the null element of $V$), we must have $t - s = 0$, so $tv = sv \Rightarrow t = s$. Therefore, the mapping is injective.

share|cite|improve this answer
Thanks. Do you know a good introductory book for Linear Algebra? – José Carlos Rocha Apr 21 '13 at 6:44
Lay's Linear Algebra and Its Applications is the book my university recommends, but I haven't used it myself so I don't know what it is like. – Michael Albanese Apr 21 '13 at 7:00

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.