Pertanyaan

A = ( 1 3 2 4 ) , B = ( 2 4 1 3 ) , C = ( 2 2 0 1 ) , dan D = ⎝ ⎛ 1 3 4 2 2 5 ⎠ ⎞ Tentukan : e. A − 1 B − 1 + ( BC ) − 1

$A = (1324), B = (2413), C = (2201), dan D = ⎝ ⎛ 134225 ⎠ ⎞$

Tentukan :

e. $A^{- 1} B^{- 1} + (BC)^{- 1}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

hasil operasi tersebut adalah .

hasil operasi tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 17 over 4 end cell cell 7 over 4 end cell row cell negative 1 fourth end cell cell 1 fourth end cell end table close parentheses end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 17 over 4 end cell cell 7 over 4 end cell row cell negative 1 fourth end cell cell 1 fourth end cell end table close parentheses end cell end table

Pembahasan

Ingat rumus invers, penjumlahan dan perkalian matriks berikut: Berdasarkan rumus tersebut, maka Jadi, hasil operasi tersebut adalah .

Ingat rumus invers, penjumlahan dan perkalian matriks berikut:

$open parentheses table row straight a straight b row straight c straight d end table close parentheses to the power of negative 1 end exponent equals fraction numerator 1 over denominator ad minus bc end fraction open parentheses table row straight d cell negative straight b end cell row cell negative straight c end cell straight a end table close parentheses$

Berdasarkan rumus tersebut, maka

$table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards double arrow cell A to the power of negative 1 end exponent B to the power of negative 1 end exponent equals fraction numerator 1 over denominator 4 minus 6 end fraction open parentheses table row 4 cell negative 2 end cell row cell negative 3 end cell 1 end table close parentheses fraction numerator 1 over denominator 6 minus 4 end fraction open parentheses table row 3 cell negative 1 end cell row cell negative 4 end cell 2 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 2 left parenthesis 2 right parenthesis end fraction open parentheses table row 4 cell negative 2 end cell row cell negative 3 end cell 1 end table close parentheses open parentheses table row 3 cell negative 1 end cell row cell negative 4 end cell 2 end table close parentheses end cell row blank equals cell negative 1 fourth open parentheses table row cell 12 plus 8 end cell cell negative 4 minus 4 end cell row cell negative 9 minus 4 end cell cell 3 plus 2 end cell end table close parentheses end cell row blank equals cell negative 1 fourth open parentheses table row 20 cell negative 8 end cell row cell negative 13 end cell 5 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 end cell 2 row cell 13 over 4 end cell cell negative 5 over 4 end cell end table close parentheses end cell row blank rightwards double arrow cell open parentheses B C close parentheses to the power of negative 1 end exponent equals open parentheses open parentheses table row 2 1 row 4 3 end table close parentheses open parentheses table row 2 0 row 2 1 end table close parentheses close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row cell 4 plus 2 end cell cell 0 plus 1 end cell row cell 8 plus 6 end cell cell 0 plus 3 end cell end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row 6 1 row 14 3 end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 1 over denominator 18 minus 14 end fraction open parentheses table row 3 cell negative 1 end cell row cell negative 14 end cell 6 end table close parentheses end cell row blank equals cell 1 fourth open parentheses table row 3 cell negative 1 end cell row cell negative 14 end cell 6 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 over 4 end cell cell negative 1 fourth end cell row cell negative 14 over 4 end cell cell 6 over 4 end cell end table close parentheses end cell row blank rightwards double arrow cell A to the power of negative 1 end exponent B to the power of negative 1 end exponent plus open parentheses B C close parentheses to the power of negative 1 end exponent equals open parentheses table row cell negative 5 end cell 2 row cell 13 over 4 end cell cell negative 5 over 4 end cell end table close parentheses plus open parentheses table row cell 3 over 4 end cell cell negative 1 fourth end cell row cell negative 14 over 4 end cell cell 6 over 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 plus 3 over 4 end cell cell 2 minus 1 fourth end cell row cell 13 over 4 minus 14 over 4 end cell cell negative 5 over 4 plus 6 over 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 17 over 4 end cell cell 7 over 4 end cell row cell negative 1 fourth end cell cell 1 fourth end cell end table close parentheses end cell end table$

Jadi, hasil operasi tersebut adalah .