MATRIKS DAN DETERMINAN

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# MATRIKS DAN DETERMINAN - PowerPoint PPT Presentation

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

• BALIKAN MATRIKS

Jikaterdapatmatriks A = [aij], maka

Contoh 9.11

• Penyelesaian

9.10 BalikanMatriks (Inverse of a Matrix)

Jikamatriks A = [aij] adalahmatrikspersegi n x n, maka

balikan (inverse) dari A dilambangkandengan A-1merupakan

9.10.1 Menentukanbalikanmatriksdenganrumus

terlebihdahulu.

• Setelahitugunakanrumus

Contoh 9.12

, tentukan

Penyelesaian

9.10.2 Balikanmatriksdenganmenggunakaneliminasi Gauss-Jordan

Untukmenentukanbalikanmatriks A denganeliminasi

Gauss-Jordan berartikitaharusmelakukaneliminasi

• 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

Contoh 9.13

Dari contoh 9.12, tentukan A-1denganmetodeeliminasi

Gauss-Jordan

Penyelesaian

R2 –2/3 R1

R3 –R1

R3 –6/7 R2

R1 + 2/3R2

R2 +4/7R3

R1–9/7R3