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I have problem with proofs in vector space. First is

$\vec x+(-(\vec y+\vec z))=(\vec x+(-\vec y))+(-\vec z)$

and the second

$a\cdot \vec x+b \cdot \vec y=b \cdot \vec x+a\cdot \vec y \Leftrightarrow a=b \vee \vec x=\vec y $

Could anyone help me with this? I'm sorry for my bad english.

In the second task I have:

$a\cdot \vec x+b \cdot \vec y $ I have sentece that $ \vec x = \vec y$ or $a=b$

So i'm changing $ \vec y $ on $ \vec x$

$a\cdot \vec x+b \cdot \vec x = (a+b)\vec x = (a+b) \vec y =...$

And i don't know what can i do next.

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    Yeah that's right, I forgot about that, sorry.2012-12-01

1 Answers 1

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Hints:

For the first one show that, by definition, $-(v_{1}+v_{2})=-v_{1}-v_{2}$

where $v_{i}$ are vectors.

For the second use $\alpha v-\beta v=(\alpha-\beta)v$

where $\alpha,\beta$ are scalars, $v$ is a vector.

Also use $a-b=-(b-a)$

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    @Emil - I think you should edit the post and add the details on what you did so it will be possible to comment n it. its hard to say what you did there2012-12-02