## Maximize the Dimension of the Null Space of $A-aI$

## Problem 200

Let

\[ A=\begin{bmatrix}

5 & 2 & -1 \\

2 &2 &2 \\

-1 & 2 & 5

\end{bmatrix}.\]

Pick your favorite number $a$. Find the dimension of the null space of the matrix $A-aI$, where $I$ is the $3\times 3$ identity matrix.

Your score of this problem is equal to that dimension times five.

(*The Ohio State University Linear Algebra Practice Problem*)

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