- #1

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## Homework Statement

Let T[tex]\in[/tex]L(V,V). Prove that T[tex]^{2}[/tex]=0 iff T(V)[tex]\subset[/tex]n(T).

## Homework Equations

dim T(V) + dim n(T) = dim V comes to mind.

## The Attempt at a Solution

Honestly, I don't know where to start. I have no idea what I'm doing. My book and my professor are both utterly useless and I'm frustrated at how badly I am failing at this.