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Tentukan determinan dari matriks H = ⎣ ⎡ ​ 2 3 6 ​ − 1 4 1 ​ 5 − 2 − 3 ​ ⎦ ⎤ ​ ?

Tentukan determinan dari matriks  ?

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S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

determinan matriks H adalah .

determinan matriks H adalah negative 122.

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Pembahasan

Diketahui: Matriks . Ditanya : Determinan matriks H! Jawab: Dengan menggunakan konsep determinan matriks metode sarrus yaitu : Sehingga, Jadi, determinan matriks H adalah .

Diketahui:

Matriks straight H equals open square brackets table row 2 cell negative 1 end cell 5 row 3 4 cell negative 2 end cell row 6 1 cell negative 3 end cell end table close square brackets.

Ditanya :
Determinan matriks H!

Jawab:
Dengan menggunakan konsep determinan matriks 3 cross times 3 metode sarrus yaitu :

table attributes columnalign right center left columnspacing 0px end attributes row cell det open parentheses straight H close parentheses end cell equals cell open square brackets table row cell straight h subscript 11 end cell cell straight h subscript 12 end cell cell straight h subscript 13 end cell row cell straight h subscript 21 end cell cell straight h subscript 22 end cell cell straight h subscript 23 end cell row cell straight h subscript 31 end cell cell straight h subscript 32 end cell cell straight h subscript 33 end cell end table close square brackets table row cell straight h subscript 11 end cell cell straight h subscript 12 end cell row cell straight h subscript 21 end cell cell straight h subscript 22 end cell row cell straight h subscript 31 end cell cell straight h subscript 32 end cell end table end cell row blank equals cell straight h subscript 11 straight h subscript 22 straight h subscript 33 plus straight h subscript 12 straight h subscript 23 straight h subscript 31 plus straight h subscript 13 straight h subscript 21 straight h subscript 32 minus straight h subscript 13 straight h subscript 22 straight h subscript 31 minus straight h subscript 11 straight h subscript 23 straight h subscript 32 minus straight h subscript 12 straight h subscript 21 straight h subscript 33 end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell det left parenthesis straight H right parenthesis end cell equals cell open square brackets table row 2 cell negative 1 end cell 5 row 3 4 cell negative 2 end cell row 6 1 cell negative 3 end cell end table close square brackets table row 2 cell negative 1 end cell row 3 4 row 6 1 end table end cell row blank equals cell open parentheses 2 cross times 4 cross times negative 3 close parentheses plus open parentheses negative 1 cross times negative 2 cross times 6 close parentheses plus open parentheses 5 cross times 3 cross times 1 close parentheses minus open parentheses 5 cross times 4 cross times 6 close parentheses minus open parentheses 2 cross times negative 2 cross times 1 close parentheses minus open parentheses negative 1 cross times 3 cross times negative 3 close parentheses end cell row blank equals cell open parentheses negative 24 close parentheses plus 12 plus 15 minus 120 minus open parentheses negative 4 close parentheses minus 9 end cell row blank equals cell negative 122 end cell end table

Jadi, determinan matriks H adalah negative 122.

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