Questions

01

Double eigenvalues does not imply insufficient eigenvectors

What are the eigenvalues and eigenvectors of $A=\left(\begin{array}{cc}2& 0\\ 0& 2\end{array}\right)$? Are there enough to form a basis of ${\mathbb{R}}^2$?

02

Enough eigenvectors?

Does the matrix $A=\left(\begin{array}{ccc}2& 1& 0\\ 0& 2& 1\\ 0& 0& 2\end{array}\right)$ have enough eigenvectors to form a basis? If not, how many does it have?