Recall: "If and only if" two directions. Given n vectors V₁,..., V, it is possible to write one of the vectors as a lin- ear combination of the other n - 1 vectors if and only if there exist scalars C1,..., Cn, not all zero, such that Vi+c2+…+CV=0

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.