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Mathematik-Online problems:

Problem 58: Determination of Kernel and Image 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
Given the matrix

$\displaystyle A=\left(\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right). $

Let $ \alpha: \mathbb{R}^3\longrightarrow\mathbb{R}^3$ be the linear map, defined by $ x\longmapsto Ax$. Determine the kernel and the image of $ \alpha$ and show, that

$\displaystyle {\mathrm{Ker}}\, \alpha \perp {\mathrm{Im}}\, \alpha $

holds.
(Authors: Apprich/Höfert)

Solution:

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  automatisch erstellt am 14. 10. 2004