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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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1 Answer

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 $tv = sv \Rightarrow t = s$, so the mapping is injective.

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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
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