Question

How to find whether the given vector is an eigen vector of a matrix?

Answer 1

igenvector of A=[−3−318]A=[−31−38]? If yes, find the eigenvalue.
The way that I approached this question is to find eigenvalues, then use eigenvalues to verify whether vv is an eigenvector of the matrix. Here is how I find the eigenvalues:

∴λdet(A−λI)=det([−3−318]−[λ00λ])=det([−3−λ−318−λ])=(−3−λ)(8−λ)−(−3)=12(5±109−−−√)