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Quizz vector spaces

Quizz vector spaces
--- Introduction ---

This module contains 11 training exercises on basic notions of
vector spaces.

Students may use them as a training tool for a better memorization of the lesson,
while teachers may put them into a work sheet with activated time limit, so that
proficiency can be tested.

Two subsets

Let be a vector space. We have two subsets of ,
and
, having respectively and elements. Answer:

If , then
.

If , then
.

Def dependence

Fill in:

Def generation

Fill in:

Dependence

Let
be a vector space,
a non-empty subset.

. True?

. True?

Dimension and elements

Answer:

Let
be a vector space,
a finite subset that . If ,
.

Dim subspace by system

Let E be a sub-vector space of R^{} defined by a homogeneous linear system. This system is composed of equations, and the rank of the coefficient matrix of this system is equal to . What is the dimension of E?

Generated subspace

Let
be a vector subspace of
generated by a subset
of elements. What can be said of the dimension of
?

dim(
) is
equal to
.

Inclusion

Let
be a vector space,
,
two distinct finite subsets with
.

. True?

. True?

Set

Let
be a vector space of dimension ,
a subset of elements.

Can
be linearly independent?

Can
generate
?

Can
be a basis of
?

Set and basis

Let
be a vector space of dimension ,
a subset of
elements. Among the following properties, which ones ?

.

.

.

.

Generating subsets

Let
be a vector space generated by a set
= {
}. Given that there is a relation

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Description: elementary questions on vector spaces. serveur web interactif avec des cours en ligne, des exercices interactifs en sciences et langues pour l'enseigment primaire, secondaire et universitaire, des calculatrices et traceurs en ligne

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