This module is an exercise of linear algebra, on the generation of the vector space ${\mathbb{R}}^{n}$ by a given set of vectors.

The exercise first gives you the vectors (randomly generated), and automatically computes the rank of the matrix formed by these vectors. You have to determine, according to these data, whether the vectors generate the whole space, and give the reason for your reply.

A second question will be asked if the exercise is in an advanced mode. This second question depends on the first reply: if you think that the vectors generate the space, you will be presented another vector, and should express it as a linear combination of the given generator vectors. Otherwise, you should find a vector in the space which is not in the subspace generated by the given vectors.

You may go to work on the exercise, by choosing the level of difficulty:

- 1
- 2
- 3
- 4
- 5
- 6

Other exercises on: Vector space Matrix Basis Vectors Linear algebra

The most recent versionPlease take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.

- Description: does a given set of vectors generate the whole vector space?. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: wims, mathematics, mathematical, math, maths, interactive mathematics, interactive math, interactive maths, mathematic, online, calculator, graphing, exercise, exercice, puzzle, calculus, K-12, algebra, mathématique, interactive, interactive mathematics, interactive mathematical, interactive math, interactive maths, mathematical education, enseignement mathématique, mathematics teaching, teaching mathematics, algebra, geometry, calculus, function, curve, surface, graphing, virtual class, virtual classes, virtual classroom, virtual classrooms, interactive documents, interactive document, algebra, linear_algebra, vector_space, matrix, basis, vectors, linear_algebra,linear_system,rank