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Mathematics-Online problems:

Interactive Problem 42: Eigenvalues/Determinant/Rank

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
Given the matrices

$\displaystyle A=\left(\begin{array}{ccc} 1+\sqrt{3} & 0 & 1 \\ 0 & 2 & 0 \\ 1 &... ...(\begin{array}{rrr} 2 & -1 & 2 \\ -2 & 3 & -5 \\ 1 & 4 & -6\end{array}\right). $

a)
Declare the eigenvalues of $ A$ in ascending order:

$ \lambda_1=$ $ \lambda_2=$ $ \lambda_3=$

b)
Find:

$ \operatorname{rank}\, A=$ $ \operatorname{det}\, B =$
$ \operatorname{trace}\,(B^{-1}AB)=$ $ \operatorname{det}\,(B^{-1}A)=$


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