Hello! I have just another problem I can't figure out how to solve:(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Consider a homomorphism of short exact sequences (it's all vector spaces):

[PLAIN]http://img814.imageshack.us/img814/9568/seq.png [Broken]

Prove that:

(1) [tex]\sigma[/tex] is surjective iff [tex]\rho[/tex] is injective.

(2) [tex]\sigma[/tex] is injective iff [tex]\rho[/tex] is surjective.

2. Relevant equations

Earlier parts of the exercise:

(1) [tex]\psi_2 (\hbox{Im } \sigma)=\hbox{Im } \tau[/tex]

There was also another,

(2) [tex]\phi_1(\ker \rho)=\ker \sigma[/tex],

but this is wrong, I'm afraid.

3. The attempt at a solution

I'm deeply sorry, but I have no idea where to start.

Thanks in advance for any hints!

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# Homework Help: Short Exact Sequences

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