Question
Find eigenvalues of matrix:
$$ A = \left[ \begin{matrix}3&-3\\-2&-4\end{matrix} \right] $$Answer
The eigenvalues of matrix A are:
$$ \lambda_1 = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 73 }}{ 2 } ~ \text{ and } ~ \lambda_2 = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 73 }}{ 2 } $$Explanation
Step 1 : The characteristic polynomial for matrix A is:
$$ p(\lambda) = \lambda^2+\lambda-18 $$
Step 2 : Eigenvalues are roots of the characteristic polynomial, so the equation
$$ \lambda^2+\lambda-18 = 0 $$yields the above eigenvalues.
( click here to view an explanation on how to solve this equation.)
This page was created using
Eigenvalues calculator