Linear Equations and Matrices

  • Jin Ho Kwak
  • Sungpyo Hong

Abstract

One of the central motivations for linear algebra is solving systems of linear equations. We thus begin with the problem of finding the solutions of a system of m linear equations in n unknowns of the following form:
$$\left\{ {\begin{array}{*{20}{c}} \hfill {{{a}_{{11}}}{{x}_{1}} + {{a}_{{12}}}{{x}_{2}} + \cdots + {{a}_{{1n}}}{{x}_{n}} = {{b}_{1}}} \\ \hfill {{{a}_{{21}}}{{x}_{1}} + {{a}_{{22}}}{{x}_{2}} + \cdots + {{a}_{{2n}}}{{x}_{n}}\mathop{{ = {{b}_{2}}}}\limits_{ \vdots } } \\ \hfill {{{a}_{{m1}}}{{x}_{1}} + {{a}_{{m2}}}{{x}_{2}} + \cdots + {{a}_{{mn}}}{{x}_{n}} = {{b}_{m}},} \\ \end{array} } \right.$$
where x 1, x 2, ..., x n are the unknowns and a ij ’s and b i ’s denote constant (real or complex) numbers.

Keywords

Free Variable Triangular Matrix Gaussian Elimination Permutation Matrix Elementary Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Jin Ho Kwak
    • 1
  • Sungpyo Hong
    • 1
  1. 1.Department of MathematicsPohang University of Science and TechnologyPohangThe Republic of Korea

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