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Matrix Algebra and System of Linear Equations
Abstract
This chapter deals with an elementary introduction to matrix algebra. First, we give a brief introduction to vectors and vector operations, then we discuss basic materials on matrices, determinants, their properties and the solution of linear system of equations. We also consider the solution of the systems of linear equations by using the inverse of the coefficient matrix of the given system of equations. We introduce the Gaussian method based on a series of algebraic operations which are compatible with computer software. Regarding the importance of eigenvalues, the eigenvalues and eigenvectors, which are numbers and vectors associated with square matrices. The last section of this chapter considers some applications of matrices to several examples we encounter in industry or applied mathematics.
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