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Mathematik-Online problems:

Problem 520: Subspaces of Vector Spaces

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
Analyse in each case, if $ U$ is a subspace of the real vector space $ V$.
a)
$ V = { }$ Set of all sequences of real numbers
$ U = { }$ Set of all bounded sequences of real numbers
b)
$ V=\mathbb{R}^{2}$
$ U=\left\{(x,y) \in\mathbb{R}^{2}: \;\, x<y\right\}$
c)
$ V = { }$ Set of the continuous functions $ f:\mathbb{R}\longrightarrow \mathbb{R}$
$ U=\left\{f\in V: \;\, f(1)=f(2)\right\}$
d)
$ V=\mathbb{R}^{4}$
$ U_{a}=\left\{(x_{1},x_{2},x_{3},x_{4})\in\mathbb{R}^{4}: \;\, x_{1}^{2}+x_{2}^{2}=a\right\}$, for $ a\in \mathbb{R}$

(Authors: Wipper/Höfert)
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  automatisch erstellt am 12.  3. 2018