how to extend a basis - Mathematics Stack Exchange Put your independent vectors in a list, which you then complete with a generating set for the whole space, as described in the answer by Matt Pressland (the standard basis is the most obvious choice for a generating set for $\Bbb R^n$) Now for each vector in the list in turn, see if the set of vectors in the list up to and including it is linearly dependent If it is, keep the vector, if it
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