Answer
$\lambda^2-6\lambda+8$
Work Step by Step
$\left| \begin{array}{cc}
\lambda-2 & 0 \\
4 & \lambda-4 \end{array}
\right|=ad-bc$
$=(\lambda-2)\times (\lambda-4)-0\times4$
$=\lambda^2-4\lambda-2\lambda+8$
$=\lambda^2-6\lambda+8$
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