EKSISTENSI PENYELESAIAN TAK TRIVIAL SISTEM PERSAMAAN LINIER HOMOGEN ATAS RING KOMUTATIF

DANIEL KRISNA SANTOSO, 080112270 (2006) EKSISTENSI PENYELESAIAN TAK TRIVIAL SISTEM PERSAMAAN LINIER HOMOGEN ATAS RING KOMUTATIF. Skripsi thesis, UNIVERSITAS AIRLANGGA.

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Official URL: http://lib.unair.ac.id

Abstract

Tujuan skripsi ini adalah menunjukkan eksistensi penyelesaian tak trivial pada Sistem Persamaan Linier (SPL) homogen atas ring komutatif. Dengan menggunakan sifat-sifat SPL, matriks, annihilator, dan rank matriks atas ring komutatif, ditunjukkan syarat agar SPL homogen atas ring komutatif mempunyai penyelesaian tak trivial. Dari pembahasan dapat diambil kesimpulan bahwa : 1. Sistem persamaan linier AX = 0 mempunyai penyelesaian tak trivial jika dan hanya jika rk (A) < n. 2. Setiap sistem persamaan linier homogen mempunyai penyelesaian tak trivial jika banyaknya persamaan kurang dari banyaknya variabel yang tidak diketahui Translation: The purpose of the script is to prove the existence of nontrivial solution on homogeneous system of linear equations over commutative ring. Moreover, by using properties of linear system of equations, matrix, annihilator, and the rank of matrix over commutative ring, it can be found the condition of homogeneous system of linear equations over commutative ring in order to has a nontrivial solution. From the discuss taken the conclusion, viz. : 1. The homogeneous system of linear equations AX = O has a nontrivial solution if and only if rk (A) < n. 2. Any homogeneous system of linear equations has a nontrivial solution if the number of equations is less than the number of unknowns.

Item Type: Thesis (Skripsi)
Additional Information: KKC KK MPM 04/07 San e
Uncontrolled Keywords: LINEAR SYSTEMS
Subjects: Q Science > QA Mathematics > QA184-205 Linear and Multilinear Algebra, Matrices
Divisions: 08. Fakultas Sains dan Teknologi > Matematika
Creators:
CreatorsEmail
DANIEL KRISNA SANTOSO, 080112270UNSPECIFIED
Contributors:
ContributionNameEmail
ContributorKuswandari, Inna;, Estuningsih, NenikUNSPECIFIED
Depositing User: Turwulandari
Date Deposited: 15 Jun 2007 12:00
Last Modified: 27 Jul 2016 10:46
URI: http://repository.unair.ac.id/id/eprint/25950
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