Math, asked by ansarskhan851, 1 year ago

Any spanning set of vectors can be reduced to a basis

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Answered by Anonymous

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⏭️A spanning list in a vector space may not be a basis because it is not linearly independent. Our next result says that given any spanning list, some (possibly none) of the vectors in it can be discarded so that the remaining list is linearly independent and still spans the vector space.

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Answered by za6715

the last Section, we established the notion of a linearly independent set of vectors in avector space V , and of a set of vectors thatspan V . We saw that any set of vectors thatspan V can be reduced to some minimal collection of linearly independent vectors; such a set is called a basis of the subspace V

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