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Mathematics-Online problems:

Interactive Problem 306: Diagonalisation and Matrix Powers

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Find the eigenvalues $ \lambda_i$ and the eigenvectors $ v_i$ of the matrix

$\displaystyle A=\frac{1}{2}\left(\begin{array}{rr} 3 & -1\\ 5 & -3\end{array}\right). $

and calculate $ A^{2222}$.


Solution:

Eigenvalues in ascending order: $ \lambda_1=$ ,      $ \lambda_2=$

$ A^{2222}=\left(\rule{0pt}{4ex}\right.$
$ \left.\rule{0pt}{4ex}\right)$.

   
(Authors: Apprich/Höfert)
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  automatically generated: 8/11/2017