## Find All the Eigenvalues and Eigenvectors of the 6 by 6 Matrix

## Problem 400

Find all the eigenvalues and eigenvectors of the matrix

\[A=\begin{bmatrix}

10001 & 3 & 5 & 7 &9 & 11 \\

1 & 10003 & 5 & 7 & 9 & 11 \\

1 & 3 & 10005 & 7 & 9 & 11 \\

1 & 3 & 5 & 10007 & 9 & 11 \\

1 &3 & 5 & 7 & 10009 & 11 \\

1 &3 & 5 & 7 & 9 & 10011

\end{bmatrix}.\]

(*MIT, Linear Algebra Homework Problem*)

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