Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online problems:

Interactive Problem 44: Matrix Representation of a Linear Map

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
Let $ \alpha: \mathbb{R}^2\longrightarrow\mathbb{R}^2$ be the linear map defined by

$\displaystyle \left(\begin{array}{r}1\\ -2\end{array}\right)\longmapsto \left(\... ...d{array}\right)\longmapsto \left(\begin{array}{r}-3\\ 6\end{array}\right) \ . $

Find the matrix representation $ A$ of $ \alpha$ with respect to the canonical basis of $ \mathbb{R}^2$. Find the integral vector $ v$ of minimal length and whose first entry is positive. Further $ v$ shall be element of $ \operatorname{Ker}\, \alpha $.

$ A=\left(\rule{0pt}{4ex}\right.$
$ \left.\rule{0pt}{4ex}\right)$

$ \quad v=\left(\rule{0pt}{4ex}\right.$
$ \left.\rule{0pt}{4ex}\right) \in \operatorname{Ker}\,\alpha $


   

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