## Proving kernel of matrix is isomorphic to 0 eigenvalue's eigenvectors

1. The problem statement, all variables and given/known data
I want to prove that the eigenvectors corresponding to the 0 eigenvalue of hte matrix is the same thing as the kernel of the matrix.

2. Relevant equations
A = matrix.
L = lambda (eigenvalues)

Ax=Lx

3. The attempt at a solution

Ax = 0 is the nullspace.

Ax = Lx
Lx = 0.
L= 0.
the eigenvectors corresponding to the 0 eigenvalue are the same as the nullspace.

Is this a sufficient enough proof?
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 Recognitions: Homework Help Science Advisor No, it's not. Maybe you have the right idea, but what you've written down doesn't make a lot of sense. The nullspace is {x : Ax = 0}. Can you write down what the set of eigenvectors corresponding to zero is?
 Isn't the the set of eigenvectors which correspond to the 0 eigenvalue?

Recognitions:
Homework Help