Norm in a Vector Space A vector space with norm $\parallel\cdot\parallel$ Satisfy for two vectors the following
$\parallel x+y\parallel=\parallel x\parallel +\parallel y\parallel$
i need to proof the fallowing statement
$\parallel \alpha x+\beta y\parallel=\alpha\parallel x\parallel +\beta\parallel y\parallel$
for all $\alpha\geq0$ and $\beta\geq0$, and also this norm it's not necessary induced by an inner product
The fact that 
$\alpha\parallel x\parallel +\beta\parallel y\parallel\geq\parallel \alpha x + \beta y\parallel$
it's clear because the property of the norm, what i can't proof it's the fact that 
$\alpha\parallel x\parallel +\beta\parallel y\parallel\leq\parallel \alpha x + \beta y\parallel$
i will appreciate any help.

To show that the norm is induced by an inner product you can show that the norm satisfies the parallelogram law and then use the polarization identity to recover the norm.
