###### Exercise2

Given an $$n\times n$$ matrix $$A\text{,}$$ an important question Question 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.

in-context