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Mathematik-Online problems:

Problem 532: Matrix Representation of a Rational Function

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
After defining $ z=x/y $ and $ w=u/v $, one can consider the map

$\displaystyle w=r(z)= \frac{az+b}{cz+d} \ \ \ \ \ ( ad-bc \neq 0) $

as a matrix multiplication

$\displaystyle \begin{pmatrix}u \\ v\end{pmatrix} = A \begin{pmatrix}x \\ y \end{pmatrix} . $

(Mind that $ A$ is uniquely defined, excepted for multiples.)
a)
Find the matrix $ A$.

b)
Find the inverse map $ z= r^{-1}(w) $ and the associated matrix.

c)
Which special matrices belong to the maps $ 3z $, $ z+7 $ and $ 1/z$.

(Authors: Höllig/Höfert)

see also:

  automatisch erstellt am 12.  3. 2018