-proof help for upcoming exam-eigenvalue

Hello,

I dont think I've posted this one before....

Prove that Null(A)={0} iff λ=0 is not an eigenvalue of A.How do i answer this question ?

And ..i dont really know how to write math proofs well..is there a general structure that I can memorise so that I may apply it when neccessary to many other proofs for linear algebra.?

thanks.

Re: -proof help for upcoming exam-eigenvalue

Hi, I would say that Null(A)=$\displaystyle \{0\}$ iff A as a square matrix is regular (because of uniqueness of the solution of system Ax=b for any b)

on the other hand $\displaystyle \lambda=0$ is an eigenvalue of the square matrix A iff A is singular

can you use that?

Re: -proof help for upcoming exam-eigenvalue

What does "0 is an eigenvalue of A" **mean**? Your result is a direct consequence of the definition.