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Mathematics-Online problems:

Interactive Problem 295: Rank, Trace and Determinant of Matrices

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}{rrr}1&2&0\\ 3&0&4\\ 0&5&6\end{array}\right), \qquad B=\left(\begin{array}{rrr}1&0&2\\ 3&0&6\\ 4&0&8\end{array}\right). $

Determine - without too long calculation:
a) $ \displaystyle\det\hspace*{0.05cm}(A^{-1})$ =                  b) $ \displaystyle\det\left(AB\right)$ =
c) $ \operatorname{Rg}\left(A^{\rm {t}}AB\right)$ =          d) $ \operatorname{Tr}\left(A^{-1}BA\right) $ =
e) $ \displaystyle\operatorname{Rg}\left(B^{\,\rm {t}}A^{\rm {t}}A\right)$ =          

(Round the results off to four decimal places)
   

(Authors: Bossle/Höfert)
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  automatically generated: 3/12/2018