Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

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)

see also:



  automatisch erstellt am 12.  3. 2018