Thread: [SOLVED] Find nullspace given eigenvalues

Hi,
Suppose A has eigenvalues 0,3,5 with independent eigenvectors u,v,w.
Give a basis for the nullspace and a basis for the column space.
Could you please explain this to me?
Thanks

Hello,

Originally Posted by tbyou87

Hi,
Suppose A has eigenvalues 0,3,5 with independent eigenvectors u,v,w.
Give a basis for the nullspace and a basis for the column space.
Could you please explain this to me?
Thanks

The nullspace maps to the zero element.

Since A has an eigenvalue 0 with associated eigenvector u, we have :

So u belongs to the nullspace, along with the null vector which always belongs to the nullspace.

The other ones form a basis for the column space.