Question
Find eigenvalues of matrix:
$$ A = \left[ \begin{matrix}2&3&4\\3&4&2\\4&2&3\end{matrix} \right] $$Answer
The eigenvalues of matrix A are:
$$ \lambda_1 = 9 ~ \text{ , } ~ \lambda_2 = -\sqrt{ 3 } ~ \text{ and } ~ \lambda_3 = \sqrt{ 3 } $$Explanation
Step 1 : The characteristic polynomial for matrix A is:
$$ p(\lambda) = -\lambda^3+9\lambda^2+3\lambda-27 $$
Step 2 : Eigenvalues are roots of the characteristic polynomial, so the equation
$$ -\lambda^3+9\lambda^2+3\lambda-27 = 0 $$yields the above eigenvalues.
( click here to view an explanation on how to solve this equation.)
This page was created using
Eigenvalues calculator