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The characteristic polynomial $f(\lambda)$ of the $3 \times 3$ matrix \[ \left( \begin{array}{ccc} a & b & c <br />d & e & f <br />g & h & i \end{array} \right)\] is given by the equation \[ f(\lambda) = \left| \begin{array}{ccc} \lambda - a & -b & -c <br />-d & \lambda - e & -f <br />-g & -h & \lambda - i \end{array} \right|.\]
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