# Linear Algebra Proof of Injective Function

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.

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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.