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:

Def dependence

Fill in:


Def generation

Fill in:


Dependence

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


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 .


Set

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


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
,
which of the following subsets already generate ?

Other exercises on: vector spaces   linear algebra  


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Description: elementary questions on vector spaces. interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: interactive mathematics, interactive math, server side interactivity, nice sophia antipolis university, algebra, linear_algebra, vector_space, basis, dimension, linear_systems