MATH1231 - Linear Combinations

A linear combination of a and b is anything that can be produced by taking a multiple of the first and adding it to a multiple of the second.

For a Vector Space v, and a vector u є V, and S = {v1, v2, … , vn}

If we can find scalars

λ1, λ2, … , λn

such that

u = λ1v1 + λ2v2 + … + λnvn

then u is a linear combination of the elements of S.