What Does "span" Mean in Linear Algebra?

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"Span" in linear algebra refers to the set of all linear combinations of vectors in a vector space. The span of a set of vectors S is the intersection of all subspaces within the given vector space V that contain vectors in S.

If every vector in vector space V can be written as a linear combination of the vectors in the set S, then S spans V. The set S = {(0, 1, 1,) (1, 0, 1) (1, 1, 0)} can be used to write a vector v = (x, y, z) in vector space V, as a linear combination of vectors in S indicating that S spans V.