Pertanyaan

Diketahui dan . Buktikan bahwa: a. b.

Diketahui P equals open parentheses table row 10 19 row cell negative 1 end cell cell negative 2 end cell end table close parentheses dan Q equals open parentheses table row cell space space 4 end cell cell negative 9 end cell row cell negative 3 end cell cell space space 7 end cell end table close parentheses . Buktikan bahwa:

a. open parentheses P Q close parentheses to the power of negative 1 end exponent equals Q to the power of negative 1 end exponent P to the power of negative 1 end exponent
b. open parentheses Q P close parentheses to the power of negative 1 end exponent equals P to the power of negative 1 end exponent Q

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

A. Acfreelance

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa open parentheses Q P close parentheses to the power of negative 1 end exponent equals P to the power of negative 1 end exponent Q

Pembahasan

Untuk membuktikan hal tersebut kita perlu mengingat invers matriks berordo 2 × 2 dan memperhatikan operasi perkalian matriks dengan matriks. Jika A = ( a c b d ) , maka A − 1 = a d − c b 1 ( d − c − b a ) Diketahui dan . a. Dengan demikian, terbukti bahwa . b. Dengan demikian, terbukti bahwa .

Untuk membuktikan hal tersebut kita perlu mengingat invers matriks berordo $2 \times 2$ dan memperhatikan operasi perkalian matriks dengan matriks.

$Jika A = (a c b d), maka A^{- 1} = \frac{1}{a d - c b} (d - c - b a)$

a. open parentheses P Q close parentheses to the power of negative 1 end exponent equals Q to the power of negative 1 end exponent P to the power of negative 1 end exponent

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses P Q close parentheses to the power of negative 1 end exponent equals Q to the power of negative 1 end exponent P to the power of negative 1 end exponent space space space space space space space space space space space open parentheses open parentheses table row 10 19 row cell negative 1 end cell cell negative 2 end cell end table close parentheses open parentheses table row 4 cell negative 9 end cell row cell negative 3 end cell 7 end table close parentheses close parentheses to the power of negative 1 end exponent equals open parentheses table row 4 cell negative 9 end cell row cell negative 3 end cell 7 end table close parentheses to the power of negative 1 end exponent open parentheses table row 10 19 row cell negative 1 end cell cell negative 2 end cell end table close parentheses to the power of negative 1 end exponent open parentheses open parentheses table row cell 40 plus left parenthesis negative 57 right parenthesis end cell cell space minus 90 plus 133 end cell row cell negative 4 plus 6 end cell cell space 9 plus left parenthesis negative 14 right parenthesis end cell end table close parentheses close parentheses to the power of negative 1 end exponent equals 1 over 1 open parentheses table row 7 9 row 3 4 end table close parentheses fraction numerator 1 over denominator negative 1 end fraction open parentheses table row cell negative 2 end cell cell negative 19 end cell row 1 10 end table close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses table row cell negative 17 end cell 43 row 2 cell negative 5 end cell end table close parentheses to the power of negative 1 end exponent equals open parentheses table row 7 9 row 3 4 end table close parentheses open parentheses table row 2 19 row cell negative 1 end cell cell negative 10 end cell end table close parentheses space space space space space fraction numerator 1 over denominator negative 17. negative 5 minus 43.2 end fraction open parentheses table row cell negative 5 end cell cell negative 43 end cell row cell negative 2 end cell cell negative 17 end cell end table close parentheses equals open parentheses table row 7 9 row 3 4 end table close parentheses open parentheses table row 2 19 row cell negative 1 end cell cell negative 10 end cell end table close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space fraction numerator 1 over denominator negative 1 end fraction open parentheses table row cell negative 5 end cell cell negative 43 end cell row cell negative 2 end cell cell negative 17 end cell end table close parentheses equals open parentheses table row cell 14 plus left parenthesis negative 9 right parenthesis end cell cell 133 plus left parenthesis negative 90 right parenthesis end cell row cell 6 plus left parenthesis negative 4 right parenthesis end cell cell space 57 plus left parenthesis negative 40 right parenthesis end cell end table close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses table row 5 cell space space 43 end cell row 2 cell space space 17 end cell end table close parentheses equals open parentheses table row 5 cell space space 43 end cell row 2 cell space space 17 end cell end table close parentheses$

Dengan demikian, terbukti bahwa open parentheses P Q close parentheses to the power of negative 1 end exponent equals Q to the power of negative 1 end exponent P to the power of negative 1 end exponent .

b. open parentheses Q P close parentheses to the power of negative 1 end exponent equals P to the power of negative 1 end exponent Q

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses Q P close parentheses to the power of negative 1 end exponent equals P to the power of negative 1 end exponent Q to the power of negative 1 end exponent space space space space space space space space space space space open parentheses open parentheses table row 4 cell negative 9 end cell row cell negative 3 end cell 7 end table close parentheses open parentheses table row 10 19 row cell negative 1 end cell cell negative 2 end cell end table close parentheses close parentheses to the power of negative 1 end exponent equals open parentheses table row 10 19 row cell negative 1 end cell cell negative 2 end cell end table close parentheses to the power of negative 1 end exponent open parentheses table row 4 cell negative 9 end cell row cell negative 3 end cell 7 end table close parentheses to the power of negative 1 end exponent open parentheses table row cell 40 plus 9 end cell cell 76 plus 18 end cell row cell negative 30 plus left parenthesis negative 7 right parenthesis end cell cell negative 57 plus left parenthesis negative 14 right parenthesis end cell end table close parentheses to the power of negative 1 end exponent equals fraction numerator 1 over denominator negative 1 end fraction open parentheses table row cell negative 2 end cell cell negative 19 end cell row 1 10 end table close parentheses 1 over 1 open parentheses table row 7 9 row 3 4 end table close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses table row 49 94 row cell negative 37 end cell cell negative 71 end cell end table close parentheses to the power of negative 1 end exponent equals open parentheses table row 2 19 row cell negative 1 end cell cell negative 10 end cell end table close parentheses open parentheses table row 7 9 row 3 4 end table close parentheses space space space space space space space space space space space space space space space space space space space space space space space space fraction numerator 1 over denominator negative 1 end fraction open parentheses table row cell negative 71 end cell cell negative 94 end cell row 37 49 end table close parentheses equals open parentheses table row 2 19 row cell negative 1 end cell cell negative 10 end cell end table close parentheses open parentheses table row 7 9 row 3 4 end table close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space fraction numerator 1 over denominator negative 1 end fraction open parentheses table row cell negative 71 end cell cell negative 94 end cell row 37 49 end table close parentheses equals open parentheses table row cell 14 plus 57 end cell cell 18 plus 76 end cell row cell left parenthesis negative 7 right parenthesis plus left parenthesis negative 30 right parenthesis end cell cell left parenthesis negative 9 right parenthesis plus left parenthesis negative 40 right parenthesis end cell end table close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses table row 71 94 row cell negative 37 end cell cell negative 49 end cell end table close parentheses equals open parentheses table row 71 94 row cell negative 37 end cell cell negative 49 end cell end table close parentheses$

Dengan demikian, terbukti bahwa open parentheses Q P close parentheses to the power of negative 1 end exponent equals P to the power of negative 1 end exponent Q .

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

1.0 (1 rating)

Miftahul Farij

Jawaban tidak sesuai

Pertanyaan serupa

Kerjakan operasi matriks berikut ini : Diketahui Matriks A = ( 2 4 3 5 ) ,Matriks B = ( 6 8 7 9 ) , danMatriks C = ( 0 − 2 1 − 3 ) , hitunglah nilai: h. Matriks ( B × C ) = ....

5.0

Jawaban terverifikasi

Jika , , dan serta ,maka nilai dari a − b 2 adalah ….

5.0

Jawaban terverifikasi

Diketahui dan Hasil dari M × I − N T = ....

0.0

Jawaban terverifikasi

Diketahui dan . Hasil dari N × I − M T = ....

0.0

Jawaban terverifikasi

Riani adalah seorang anak penjual bakpia. Dia membantu ibunya menjual bakpia dengan membawa setiap harinya dengan cara membawanya ke sekolah. Bakpia yang dijual oleh Riani ada dua macam yaitu bakpia i...

0.0

Jawaban terverifikasi