Question
Find eigenvectors of matrix:
$$ A = \left[ \begin{matrix}5&-2\\-3&4\end{matrix} \right] $$Answer
The eigenvectors and eigenvalues of matrix A are:
| Eigenvalue | Eigenvector |
| $ 7 $ | $ \begin{bmatrix} 1 \cr -1 \end{bmatrix} $ |
| $ 2 $ | $ \begin{bmatrix} 1 \cr {{3}\over{2}} \end{bmatrix} $ |
Explanation
Step 1 : Find characteristic polynomial $ p(\lambda) $:
$$ p(\lambda) = \lambda^2-9\lambda+14 $$Step 2 : Find the eigenvalues by solving the characteristic equation $ \lambda^2-9\lambda+14 = 0. $
The eigenvalues are
$$ \lambda_1 = 7 ~ , ~ \lambda_2 = 2 $$( click here to view an explanation on how to solve this equation.)
Step 3 : To find the associated eigenvectors ( $ x $ ), we have to solve the equation $ A x = \lambda I $.
For $ \lambda_ 0 = 7 $ we have $ A x = 7 I $.
For $ \lambda_ 1 = 2 $ we have $ A x = 2 I $.
This page was created using
Eigenvectors calculator