Abstract: This chapter focuses on simultaneous linear equations. A system of simultaneous linear equations is consistent if it possesses at least one solution. If no solution exists, then the system is inconsistent. A system is homogeneous if the zero vector equals to zero. However, if at least one component differs from zero, then the system is nonhomogeneous. The chapter also presents the method of substitution for obtaining solutions. The method of substitution is not an efficient way to solve simultaneous equations and it does not lend itself well to electronic computing. Computers have difficulty symbolically manipulating the unknowns in algebraic equations. Another important method for solving simultaneous linear equations is Gaussian elimination. In this method, the augmented matrix for the system is created and then, it is transformed into a row-reduced matrix using elementary row operations. This is often accomplished by using operation with each diagonal element in a matrix to create zeros in all columns directly below it, beginning with the first column and moving successively through the matrix, column by column. The system of equations associated with a row-reduced matrix can be solved by back-substitution. An elementary row operation does not alter the column rank of a matrix.
Publication Year: 1991
Publication Date: 1991-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 2
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