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  3. Formalized Mathematics
  4. Formalized Mathematics, 2008, Volume 16, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/20685
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    Pole DCWartośćJęzyk
    dc.contributor.authorPąk, Karol-
    dc.date.accessioned2026-07-30T08:31:05Z-
    dc.date.available2026-07-30T08:31:05Z-
    dc.date.issued2008-
    dc.identifier.citationFormalized Mathematics, Volume 16, Issue 1, Pages 81-90pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/20685-
    dc.description.abstractIn this paper I present the Kronecker-Capelli theorem which states that a system of linear equations has a solution if and only if the rank of its coefficient matrix is equal to the rank of its augmented matrix.pl
    dc.language.isoenpl
    dc.publisherUniversity of Białystokpl
    dc.rightsAttribution-ShareAlike 4.0 International (CC BY-SA 4.0)-
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/-
    dc.titleSolutions of Linear Equationspl
    dc.typeArticlepl
    dc.rights.holder© 2009 Karol Pąk, published by University of Białystokpl
    dc.rights.holderThis work is licensed under the Creative Commons License.pl
    dc.identifier.doi10.2478/v10037-008-0012-4-
    dc.description.AffiliationInstitute of Computer Science, University of Białystok, Polandpl
    dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990.pl
    dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.pl
    dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.pl
    dc.description.referencesCzesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643–649, 1990.pl
    dc.description.referencesCzesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529–536, 1990.pl
    dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.pl
    dc.description.referencesCzesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990.pl
    dc.description.referencesCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357–367, 1990.pl
    dc.description.referencesCzesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.pl
    dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990.pl
    dc.description.referencesKatarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475–480, 1991.pl
    dc.description.referencesKatarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711–717, 1991.pl
    dc.description.referencesEugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335–342, 1990.pl
    dc.description.referencesRobert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.pl
    dc.description.referencesTakaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83–86, 1993.pl
    dc.description.referencesKarol Pąk. Basic properties of determinants of square matrices over a field. Formalized Mathematics, 15(1):17–25, 2007.pl
    dc.description.referencesKarol Pąk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199–211, 2007.pl
    dc.description.referencesKarol Pąk and Andrzej Trybulec. Laplace expansion. Formalized Mathematics, 15(3):143-150, 2007.pl
    dc.description.referencesAndrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115–122, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883–885, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865–870, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291–296, 1990.pl
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.pl
    dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73–83, 1990.pl
    dc.description.referencesKatarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205–211, 1992.pl
    dc.description.referencesKatarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1–8, 1993.pl
    dc.description.referencesMariusz Żynel. The Steinitz theorem and the dimension of a vector space. Formalized Mathematics, 5(3):423–428, 1996.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume16pl
    dc.description.issue1pl
    dc.description.firstpage81pl
    dc.description.lastpage90pl
    dc.identifier.citation2Formalized Mathematicspl
    Występuje w kolekcji(ach):Formalized Mathematics, 2008, Volume 16, Issue 1

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