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Mathematik-Online problems:

Problem 564: Determination of a Matrix for given Eigenvalues and Eigenvectors


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

The symmetric matrix $ A$ shall have the eigenvalues

$\displaystyle \lambda_1=1, \quad \lambda_2=-1, \quad \lambda_3=2 $

and the corresponding eigenvectors

$\displaystyle v_1=\begin{pmatrix}1\\ 0\\ -1\end{pmatrix} \ , \
v_2=\begin{pmatrix}1\\ 1\\ 1\end{pmatrix} \ , \
v_3=\begin{pmatrix}-1\\ 2\\ -1\end{pmatrix} \ .
$

a)
Find $ A$.
b)
Find $ A^{-1}$, $ \det(A)$, rank($ A$).
c)
Solve $ Ax=(0,1,0)^{\operatorname t}$.

(Authors: Höllig/Höfert)

see also:



  automatisch erstellt am 12.  3. 2018