Mathematik-Online problems: Problem 564: Determination of a Matrix for given Eigenvalues and Eigenvectors

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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

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

(Authors: Höllig/Höfert)

see also:

Keyword: Matrix
Keyword: Eigenvalue
Keyword: Eigenvector

automatisch erstellt am 12. 3. 2018