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MATRIKS DAN DETERMINAN

MATRIKS DAN DETERMINAN. ADJOIN MATRIKS BALIKAN MATRIKS. 9.9 Adjoin Matriks. Jika terdapat matriks A = [ aij ], maka. Contoh 9.11. , tentukan adjoin A. Penyelesaian. 9.10 Balikan Matriks ( Inverse of a Matrix ). Jika matriks A = [ a ij ] adalah matriks persegi n x n, maka

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MATRIKS DAN DETERMINAN

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  1. MATRIKS DAN DETERMINAN • ADJOIN MATRIKS • BALIKAN MATRIKS

  2. 9.9 Adjoin Matriks Jikaterdapatmatriks A = [aij], maka Contoh 9.11 , tentukan adjoin A • Penyelesaian

  3. 9.10 BalikanMatriks (Inverse of a Matrix) Jikamatriks A = [aij] adalahmatrikspersegi n x n, maka balikan (inverse) dari A dilambangkandengan A-1merupakan matriks n x n sehinggamemenuhi 9.10.1 Menentukanbalikanmatriksdenganrumus

  4. Salahsatucarauntukmenentukanbalikanmatriksadalahdengan mencari adjoin dandeterminandarimatriks yang dicaribalikannya terlebihdahulu. • Setelahitugunakanrumus Contoh 9.12 , tentukan Penyelesaian

  5. 9.10.2 Balikanmatriksdenganmenggunakaneliminasi Gauss-Jordan Untukmenentukanbalikanmatriks A denganeliminasi Gauss-Jordan berartikitaharusmelakukaneliminasi matriks A menjadibentukeselonbaristereduksi. • Misal A adalahmatriks non-singular n x n. • AB = I jikadanhanyajika B =A-1 Bukti AB = I A-1 AB = A-1 I  IB = A-1 B = A-1atau A|I  AB |B  I|A-1 Berarti, jikakitaberhasilmengeliminasi A|I menjadi I|X, makakitadapatmemastikanbahwa X = A-1

  6. Contoh 9.13 Dari contoh 9.12, tentukan A-1denganmetodeeliminasi Gauss-Jordan Penyelesaian R2 –2/3 R1 R3 –R1 R3 –6/7 R2

  7. R1 + 2/3R2 R2 +4/7R3 R1–9/7R3

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