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Mathematik-Online problems:

Problem 27: 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}^4\longrightarrow\mathbb{R}^4$ be the linear map defined by

$\displaystyle \begin{array}{rclrcl} (1, 2, -3, -2)^{{\operatorname t}} & \longm... ...ratorname t}} & \longmapsto & (0, 2, 3, -3)^{{\operatorname t}}\ . \end{array} $

Find the matrix representation of $ \alpha$
a)
with respect to the canonical basis $ e_1, e_2, e_3, e_4$,
b)
with respect to the basis $ b_1=(1,0,0,0)^{{\operatorname t}}$, $ b_2=(1,1,0,0)^{{\operatorname t}}$, $ b_3=(1,1,1,0)^{{\operatorname t}}$, $ b_4=(1,1,1,1)^{{\operatorname t}}$.

(Authors: Werner/Kimmerle/Apprich/Höfert)

see also:

[Solutions]
  automatisch erstellt am 14. 10. 2004