What Does "span" Mean in Linear Algebra?

What Does "span" Mean in Linear Algebra?

What Does "span" Mean in Linear Algebra?

"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.