Do Vectors Form a Basis
Online calculator to check if vectors form a basis.
This online calculator allows you to easily check if the given set of vectors forms a basis (check linear independence of vectors).
Linear Independence of Vectors
This online service allows you to determine if the entered vectors can be a basis. A necessary and sufficient condition for forming a basis is the linear independence of vectors, where none of them can be expressed through a combination of the others. This principle forms the basis of solving this task in this calculator. There is a convenient interface for entering vectors, specified either by coordinates of vectors or by coordinates of points of the beginning and end of vectors, as well as the ability to greatly change the vector space: from 2 to 6.
In n-dimensional space, if given n basis vectors, any other vectors of the space can be expressed through them, so it is very important to choose the basis correctly.