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Pertanyaan

Jika matriks A = ( 2 4 ​ 3 − 4 ​ ) dan C = ( − 1 − 1 ​ 3 5 ​ ) , maka determinan matriks A × C − 1 adalah ...

Jika matriks  dan , maka determinan matriks  adalah ...

  1. negative 40

  2. negative 10

  3. 10

  4. 20

  5. 30

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S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

jawaban yang benar adalah C.

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Pembahasan

Tentukan terlebih dahulu matriks dari . Invers matriks berlaku: Diperoleh penyelesaiannya yaitu: Kemudian tentukan determinan dari matriks . Determinan matriks berlaku: Sehingga diperoleh: Maka determinan matriks adalah . Oleh karena itu, jawaban yang benar adalah C.

Tentukan terlebih dahulu matriks dari A cross times C to the power of negative 1 end exponent.

Invers matriks 2 cross times 2 berlaku:

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open parentheses table row a b row c d end table close parentheses end cell row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator open vertical bar A close vertical bar end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator a d minus b c end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses end cell end table

Diperoleh penyelesaiannya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell A cross times C to the power of negative 1 end exponent end cell equals cell open parentheses table row 2 3 row 4 cell negative 4 end cell end table close parentheses open parentheses table row cell negative 1 end cell 3 row cell negative 1 end cell 5 end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row 2 3 row 4 cell negative 4 end cell end table close parentheses times fraction numerator 1 over denominator negative 1 open parentheses 5 close parentheses minus 3 open parentheses negative 1 close parentheses end fraction open parentheses table row 5 cell negative 3 end cell row 1 cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 3 row 4 cell negative 4 end cell end table close parentheses times fraction numerator 1 over denominator negative 5 plus 3 end fraction open parentheses table row 5 cell negative 3 end cell row 1 cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 3 row 4 cell negative 4 end cell end table close parentheses times fraction numerator 1 over denominator negative 2 end fraction open parentheses table row 5 cell negative 3 end cell row 1 cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 3 row 4 cell negative 4 end cell end table close parentheses open parentheses table row cell negative 1 half open parentheses 5 close parentheses end cell cell negative 1 half open parentheses negative 3 close parentheses end cell row cell negative 1 half open parentheses 1 close parentheses end cell cell negative 1 half open parentheses negative 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 3 row 4 cell negative 4 end cell end table close parentheses open parentheses table row cell negative 5 over 2 end cell cell 3 over 2 end cell row cell negative 1 half end cell cell 1 half end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 open parentheses negative 5 over 2 close parentheses plus 3 open parentheses negative 1 half close parentheses end cell cell 2 open parentheses 3 over 2 close parentheses plus 3 open parentheses 1 half close parentheses end cell row cell 4 open parentheses negative 5 over 2 close parentheses plus open parentheses negative 4 close parentheses open parentheses negative 1 half close parentheses end cell cell 4 open parentheses 3 over 2 close parentheses plus open parentheses negative 4 close parentheses open parentheses 1 half close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 minus 3 over 2 end cell cell 3 plus 3 over 2 end cell row cell negative 10 plus 2 end cell cell 6 minus 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative fraction numerator 5 open parentheses 2 close parentheses over denominator 2 end fraction minus 3 over 2 end cell cell fraction numerator 3 open parentheses 2 close parentheses over denominator 2 end fraction plus 3 over 2 end cell row cell negative 8 end cell 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 10 over 2 minus 3 over 2 end cell cell 6 over 2 plus 3 over 2 end cell row cell negative 8 end cell 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 13 over 2 end cell cell 9 over 2 end cell row cell negative 8 end cell 4 end table close parentheses end cell end table

Kemudian tentukan determinan dari matriks A cross times C to the power of negative 1 end exponent.

Determinan matriks 2 cross times 2 berlaku:

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open parentheses table row a b row c d end table close parentheses end cell row cell open vertical bar A close vertical bar end cell equals cell open vertical bar table row a b row c d end table close vertical bar end cell row blank equals cell a d minus b c end cell end table

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell A cross times C to the power of negative 1 end exponent end cell equals cell open parentheses table row cell negative 13 over 2 end cell cell 9 over 2 end cell row cell negative 8 end cell 4 end table close parentheses end cell row cell open vertical bar A cross times C to the power of negative 1 end exponent close vertical bar end cell equals cell open vertical bar table row cell negative 13 over 2 end cell cell 9 over 2 end cell row cell negative 8 end cell 4 end table close vertical bar end cell row blank equals cell negative 13 over 2 open parentheses 4 close parentheses minus open parentheses 9 over 2 close parentheses open parentheses negative 8 close parentheses end cell row blank equals cell negative 26 plus 36 end cell row blank equals 10 end table

Maka determinan matriks A cross times C to the power of negative 1 end exponent adalah 10.

Oleh karena itu, jawaban yang benar adalah C.

Latihan Bab

Konsep Kilat

Pengertian Matriks

Operasi Hitung Matriks

Invers Matriks

101

Mey Mey linda

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