CHAPTER 4 - MATRICES AND LINEAR SYSTEMS

Abstract

This chapter discusses matrices and linear systems. In solving a system of linear equations, the system of equations should be transformed into an equivalent system of equations that is easier to solve. A system of equations yields an equivalent system of equations if any two rows are interchanged; a row is multiplied by a nonzero constant; or a multiple of one row is added to another row. A matrix is in reduced row echelon form if: (1) a row is not made up entirely of zeros, then the leftmost nonzero number in the row is a 1; (2) there are any rows consisting entirely of zeros, they are all together at the bottom of the matrix; (3) in two successive rows, not consisting entirely of zeros, the first nonzero number in the lower row is to the right of the first nonzero number in the upper row; and (4) each column that contains the first nonzero number of some row has zeros everywhere else.