finding the eigenvector and eigenvalue

Question

|1 -1 2 |
|1 3 -3 |
|2  4  1|  what is the eigenvalue and eigenvector of this matrix

Answer 1

call the above matrix:=A.  solve the eq det(A-λI)=0 to find eigenvalues λ.

 

Then find vectors v (linearly independent) such that (A-λI)v=0.