Chapter 7 - Systems of linear equations and linear inequalities

Abstract

This chapter summarizes the systems of linear equations and linear inequalities. A system is called consistent if it has at least one solution, otherwise it is said to be inconsistent. If b = 0, the system of equations is said to be homogeneous and if b ≠ 0, it is called nonhomogeneous. A homogeneous system of equations always has a solution X = 0, which is called a trivial solution. Two systems of linear equations are said to be equivalent if they have the same set of solutions. The chapter describes that if any vector X that satisfies is called a solution to the system where the m x n matrix A = (aij) is called the coefficient matrix or the matrix of the system and the matrix Ab = (A, b) is called the augmented matrix of the system. The chapter also justifies the mathematical theorem by providing their proves.