Gleichungen

Emanuel Czuber

Chapter VII. Abschnitt in Einführung in die höhere Mathematik, 1921, pp 188-239 from Springer

Abstract: Zusammenfassung Ein System von n linearen Gleichungen mit n Unbekannten hat die allgemeine Form: (1) a 11 x 1 + a 12 x 2 + ⋯ + a 1 n x n = u 1 a 21 x 1 + a 22 x 2 + ⋯ + a 2 n x n = u 2 ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ a n 1 x 1 + a n 2 x 2 + ⋯ + a n n x n = u n $$ \begin{gathered}{a_{11}}{x_1} + {a_{12}}{x_2} + \cdots + {a_{1n}}{x_n} = {u_1} \hfill \\{a_{21}}{x_1} + {a_{22}}{x_2} + \cdots + {a_{2n}}{x_n} = {u_2} \hfill \\\cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \hfill \\{a_{n1}}{x_1} + {a_{n2}}{x_2} + \cdots + {a_{nn}}{x_n} = {u_n} \hfill \\ \end{gathered} $$ Es heißt nichthomogen, wenn wenigstens eines der absoluten Glieder u 1 u 2, • • • u n nicht Null ist. Die Koeffizienten a ik, unter welchen wir uns reelle Zahlen denken wollen, bilden eine quadratische Matrix, deren Determinante (2) R = | a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋯ ⋯ ⋯ ⋯ ⋯ a n 1 a n 2 ⋯ a n n | $$ R = \left| \begin{gathered}{a_{11}}{a_{12}} \cdots {a_{1n}} \hfill \\ {a_{21}}{a_{22}} \cdots {a_{2n}} \hfill \\\cdots \cdots \cdots \cdots \cdots \hfill \\{a_{n1}}{a_{n2}} \cdots {a_{nn}} \hfill \\ \end{gathered} \right| $$ als Determinante des Gleichungssystems (1) bezeichnet wird.

Date: 1921
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-663-16047-2_7

Ordering information: This item can be ordered from
http://www.springer.com/9783663160472

DOI: 10.1007/978-3-663-16047-2_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().