Pertanyaan

Jika A = [ 1 1 2 3 ] , B = [ 4 1 1 3 ] , maka determinan ( A ⋅ B ) − 1 = …

Jika $A = [1123], B = [4113]$ , maka determinan $(A \cdot B)^{- 1} = \dots$

H. Endah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

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determinan .

determinan open parentheses straight A times straight B close parentheses to the power of negative 1 end exponent equals 1 over 11

Pembahasan

Matriks didapatkan: Matriks didapatkan: Determinan didapatkan: Jadi,determinan .

Matriks straight A times straight B didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight A times straight B end cell equals cell open parentheses table row 1 2 row 1 3 end table close parentheses times open parentheses table row 4 1 row 1 3 end table close parentheses end cell row blank equals cell open parentheses table row 6 7 row 7 10 end table close parentheses end cell end table

Matriks open parentheses straight A times straight B close parentheses to the power of negative 1 end exponent didapatkan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight A times straight B close parentheses to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator 60 minus 49 end fraction open parentheses table row 10 cell negative 7 end cell row cell negative 7 end cell 6 end table close parentheses end cell row blank equals cell 1 over 11 open parentheses table row 10 cell negative 7 end cell row cell negative 7 end cell 6 end table close parentheses end cell row blank equals cell open parentheses table row cell 10 over 11 end cell cell fraction numerator negative 7 over denominator 11 end fraction end cell row cell fraction numerator negative 7 over denominator 11 end fraction end cell cell 6 over 11 end cell end table close parentheses end cell end table$

Determinan open parentheses straight A times straight B close parentheses to the power of negative 1 end exponent didapatkan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight A times straight B close parentheses to the power of negative 1 end exponent end cell equals cell open parentheses 10 over 11 cross times 6 over 11 close parentheses minus open parentheses fraction numerator negative 7 over denominator 11 end fraction cross times fraction numerator negative 7 over denominator 11 end fraction close parentheses end cell row blank equals cell 60 over 121 minus 49 over 121 end cell row blank equals cell 11 over 121 end cell row blank equals cell 1 over 11 end cell end table$

Jadi, determinan open parentheses straight A times straight B close parentheses to the power of negative 1 end exponent equals 1 over 11 .

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