## Eigenvalues and Eigenvectors of Matrix Whose Diagonal Entries are 3 and 9 Elsewhere

## Problem 379

Find all the eigenvalues and eigenvectors of the matrix

\[A=\begin{bmatrix}

3 & 9 & 9 & 9 \\

9 &3 & 9 & 9 \\

9 & 9 & 3 & 9 \\

9 & 9 & 9 & 3

\end{bmatrix}.\]

(*Harvard University, Linear Algebra Final Exam Problem*)