Linear equations

Abstract

Systems of linear equations occur in every branch of knowledge. We mention a few examples within Linear Algebra. Expressing b as a linear combination of a¹, a²,…, a^k is the same as solving Ax = b where A = [a¹ : a² : ⋯ : a^k]. The vectors a¹, a²,…, a^k are linearly dependent iff Ax = 0 has a non-null solution. Solution of linear equations also plays an important role in obtaining approximate solutions of non-linear equations. In this chapter, we make a systematic study of the theoretical aspects of the solution of linear equations and give some computational procedures.