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Numerical Linear Algebra with Applications by William Ford

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Chapter 2

Linear Equations

Abstract

The solution of linear systems of equations is of paramount importance in engineering and science. This chapter introduces the basics of solving linear equations using Gaussian elimination. The method is introduced systematically by covering every step in the row reduction of the augmented matrix so that the portion corresponding to the coefficient matrix is in upper triangular form. The system may have no solution or infinitely many solutions. The chapter details the use of back substitution to find the solution to the upper triangular system, if it exists. Gaussian elimination can be used to compute the inverse matrix, although the inverse is rarely computed in practice; rather, it is used for theoretical ...

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