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Systems of Linear Equations

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Foundations of Linear Algebra

Part of the book series: Kluwer Texts in the Mathematical Sciences ((TMS,volume 11))

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Abstract

The theory of finite-dimensional vector spaces was created primarily in connection with one problem, and that is the simultaneous solution of a system of k linear equations in n indeterminates over a field F of the form

$$ \begin{gathered} {a_{11}}{X_1} + ... + {a_{1n}}{X_n} = {b_1} \hfill \\ {a_{21}}{X_1} + ... + {a_{2n}}{X_n} = {b_2} \hfill \\ {a_{k1}}{X_1} + ... + {a_{kn}}{X_n} = bk \hfill \\ \end{gathered} $$

where the a ij and the b i are elements of F and the X j are indeterminates taking values in F. Such systems arise in many applications and also in many areas of mathematics.

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© 1995 Springer Science+Business Media Dordrecht

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Golan, J.S. (1995). Systems of Linear Equations. In: Foundations of Linear Algebra. Kluwer Texts in the Mathematical Sciences, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8502-6_9

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  • DOI: https://doi.org/10.1007/978-94-015-8502-6_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4592-8

  • Online ISBN: 978-94-015-8502-6

  • eBook Packages: Springer Book Archive

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