###### Exercise 2

Given an \(n\times n\) matrix \(A\text{,}\) an important question QuestionÂ 4.1.7 asks whether we can find a basis of \(\real^n\) consisting of eigenvectors of \(A\text{.}\) For each of the matrices in the previous exericse, find a basis of \(\real^n\) consisting of eigenvectors or state why such a basis does not exist.