Linear Combination is an important notion in linear algebra. 3-1. Linear Independence The goal is to understand, Linear independence Uniqueness of a solution in a linear system Subspace, basis, and dimension Column space and rank Uniqueness of Solution of Ax = b If the solution exists for Ax = b, when it is unique? It is unique when a1, a2, and a3 are linearly independent Infinitely many solutio..