Is x in the nullspace of A an eigenvector of A?

[sana2476]

Let x not equal to zero be a vector in the nullspace of A. Then x is an eigenvector of A.


I'm not sure how to start this proof

 

[JG89]

If x is a non-zero vector in the null space of A, then you know that A is singular, and you also know that $$\lambda = 0$$ is an eigenvalue of A since A is invertible if and only if zero is not an eigenvalue of A. That should start you off.

 

[HallsofIvy]

Saying that x is in the null space of A means that Ax= 0= 0x.