Question
Find eigenvalues of matrix:
$$ A = \left[ \begin{matrix}13&12&2\\12&13&-2\\2&-2&8\end{matrix} \right] $$Answer
The eigenvalues of matrix A are:
$$ \lambda_1 = 0 ~ \text{ , } ~ \lambda_2 = 9 ~ \text{ and } ~ \lambda_3 = 25 $$Explanation
Step 1 : The characteristic polynomial for matrix A is:
$$ p(\lambda) = -\lambda^3+34\lambda^2-225\lambda $$
Step 2 : Eigenvalues are roots of the characteristic polynomial, so the equation
$$ -\lambda^3+34\lambda^2-225\lambda = 0 $$yields the above eigenvalues.
( click here to view an explanation on how to solve this equation.)
This page was created using
Eigenvalues calculator