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## Homework Statement

Having:

[tex] \displaystyle T:V\to \mathbb{R}[/tex]

[tex] \displaystyle \dim\left( V \right)=n[/tex]

Prove that [tex] \displaystyle \dim\left( \ker \left( T \right) \right)=n\text{ or }n-1[/tex]

## Homework Equations

## The Attempt at a Solution

I would start stating the theorem of the dimensions:

[tex] \displaystyle \dim\left( V \right)=\dim\left( \ker \left( T \right) \right)+\dim\left( \operatorname{Im}\left( T \right) \right)[/tex]

But I get nowhere with that theorem. Any clue?

Thanks!