Question
Find eigenvalues of matrix:
$$ A = \left[ \begin{matrix}-1&1&-1\\8&-4&2\\-3&9&-27\end{matrix} \right] $$Answer
The eigenvalues of matrix A are:
$$ $$Explanation
Step 1 : The characteristic polynomial for matrix A is:
$$ p(\lambda) = -\lambda^3-32\lambda^2-110\lambda+60 $$
Step 2 : Eigenvalues are roots of the characteristic polynomial, so the equation
$$ -\lambda^3-32\lambda^2-110\lambda+60 = 0 $$yields the above eigenvalues.
( click here to view an explanation on how to solve this equation.)
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