Question
Find eigenvalues of matrix:
$$ A = \left[ \begin{matrix}-\frac{ 21 }{ 5 }&-\frac{ 19 }{ 5 }&\frac{ 59 }{ 5 }\\\frac{ 17 }{ 5 }&\frac{ 23 }{ 5 }&-\frac{ 33 }{ 5 }\\\frac{ 8 }{ 5 }&\frac{ 12 }{ 5 }&-\frac{ 7 }{ 5 }\end{matrix} \right] $$Answer
The eigenvalues of matrix A are:
$$ \lambda_1 = 1 ~ \text{ , } ~ \lambda_2 = 2 ~ \text{ and } ~ \lambda_3 = -4 $$Explanation
Step 1 : The characteristic polynomial for matrix A is:
$$ p(\lambda) = -\lambda^3-\lambda^2+10\lambda-8 $$
Step 2 : Eigenvalues are roots of the characteristic polynomial, so the equation
$$ -\lambda^3-\lambda^2+10\lambda-8 = 0 $$yields the above eigenvalues.
( click here to view an explanation on how to solve this equation.)
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