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:
Other exercises on: vector space matrices Basis Vectors linear algebraThe most recent version
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Description: does a given set of vectors generate the whole vector space? interactive exercises, online calculators and plotters, mathematical recreation and games
Keywords: interactive mathematics, interactive math, server side interactivity, algebra, linear algebra, matrix, vector, rank, linear dependence, linear system, vector space