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A Note on Systems of Linear Equations

Elliot, David L. (1961) A Note on Systems of Linear Equations. SIAM Review, 3 (1). pp. 66-69. ISSN 0036-1445. doi:10.1137/1003006.

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This note is a comment on reference [1] and a generalization of the method there presented. We consider a system of m linear equations in n unknowns x_1, x_2,...x_n (1) Σ^(n)_(j=1) a_(ij)x_j = c_i i=1, 2,...m, a_(ij), c_i real or A∙x=c in matrix notation. We distinguish three cases: (I) There is no finite vector x satisfying (1) (inconsistent case); (II) There is a unique vector x satisfying (1); (III) There are an infinity of vectors x satisfying (1), such that their endpoints lie on some line, plane, or higher-dimensional linear manifold.

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Additional Information:© 1961 SIAM. Received by the editors August 10, 1959.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
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Deposited On:21 Sep 2012 19:31
Last Modified:09 Nov 2021 23:07

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