1. ## [SOLVED] eigenspace

[FONT=CMR12][LEFT]What is eigenspace? this may seem like a general question but i cant find it online. I understand how to find the basis and eigenvectors, but im lost as to what the eigenspace is.

Here is the question that i am stuck on

Given that the eigenvalues of M =
2 -5 5
0 3 -1
0 -1 3
are 2, 2 and 4.
(a) Find the eigenspace corresponding to the eigenvalue 2. What is its dimension?

2. the eigenspace of an eigenvalue is the space generated by the eigenvectors coresponding to that eigenvalue. if an eigenvalue has multiplicity greater than 1, its eigenspace can also have a dimension greater than one. in your case finding the eigenspace of 2 is the same as finding a basis for the nullspace of $M-2I$