Roboguru

Diketahui matriks invers dari adalah...

Pertanyaan

Diketahui matriks A equals open square brackets table row 3 2 row 2 cell negative 1 end cell end table close square brackets space dan space B equals open square brackets table row cell negative 2 end cell 1 row 1 cell negative 1 end cell end table close square brackets invers dari A times B adalah...

  1. open square brackets table row cell 3 over 7 end cell cell 1 over 7 end cell row cell fraction numerator negative 5 over denominator 7 end fraction end cell 2 end table close square brackets

  2. open square brackets table row cell 1 over 7 end cell cell negative 3 over 7 end cell row cell fraction numerator negative 5 over denominator 7 end fraction end cell cell 1 over 7 end cell end table close square brackets

  3. open square brackets table row cell negative fraction numerator negative 3 over denominator 7 end fraction end cell cell negative 1 over 7 end cell row cell fraction numerator negative 5 over denominator 7 end fraction end cell cell 4 over 7 end cell end table close square brackets

  4. open square brackets table row cell negative 1 half end cell cell negative 1 1 half end cell row 1 2 end table close square brackets

  5. open square brackets table row cell negative 1 half end cell cell negative 1 1 half end cell row 1 2 end table close square brackets

Pembahasan Soal:

Ingat operasi perkalian matriks : open square brackets table row a b row c d end table close square brackets open square brackets table row e f row g h end table close square brackets equals open square brackets table row cell a e plus b g end cell cell a f plus b h end cell row cell c e plus d g end cell cell c f plus d h end cell end table close square brackets

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell A times B end cell equals cell open square brackets table row 3 2 row 2 cell negative 1 end cell end table close square brackets open square brackets table row cell negative 2 end cell 1 row 1 cell negative 1 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 3 left parenthesis negative 2 right parenthesis plus 2 left parenthesis 1 right parenthesis end cell cell 3 left parenthesis 1 right parenthesis plus 2 left parenthesis negative 1 right parenthesis end cell row cell 2 left parenthesis negative 2 right parenthesis plus left parenthesis negative 1 right parenthesis 1 end cell cell 2 left parenthesis 1 right parenthesis plus left parenthesis negative 1 right parenthesis left parenthesis negative 1 right parenthesis end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 4 end cell 1 row cell negative 5 end cell 3 end table close square brackets end cell end table

ingat invers matriks: open square brackets table row a b row c d end table close square brackets to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets

invers matriks A times B adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell open square brackets table row cell negative 4 end cell 1 row cell negative 5 end cell 3 end table close square brackets to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator negative 4 left parenthesis 3 right parenthesis minus 1 left parenthesis negative 5 right parenthesis end fraction open square brackets table row 3 cell negative 1 end cell row 5 cell negative 4 end cell end table close square brackets end cell row blank equals cell negative 1 over 7 open square brackets table row 3 cell negative 1 end cell row 5 cell negative 4 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 3 over 7 end cell cell 1 over 7 end cell row cell negative 5 over 7 end cell cell 4 over 7 end cell end table close square brackets end cell end table.

Jadi, tidak ada jawaban yang tepat pada pilihan jawaban.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Janatu

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 07 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Diketahui matriks dan matriks .  Invers matriks AB adalah =.......

Pembahasan Soal:

A B equals open parentheses table row 1 2 1 row 1 cell negative 1 end cell cell negative 1 end cell end table close parentheses open parentheses table row 1 cell negative 1 end cell row 1 1 row cell negative 1 end cell cell negative 2 end cell end table close parentheses  A B equals open parentheses table row cell 1 plus 2 minus 1 end cell cell negative 1 plus 2 minus 2 end cell row cell 1 minus 1 plus 1 end cell cell negative 1 minus 1 plus 2 end cell end table close parentheses  A B equals open parentheses table row 2 cell negative 1 end cell row 1 0 end table close parentheses  I n g a t space b a h w a space i n v e r s space d a r i space m a t r i k s space P equals open parentheses table row a b row c d end table close parentheses space a d a l a h space P to the power of negative 1 end exponent equals 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 comma space m a k a  open parentheses A B close parentheses to the power of negative 1 end exponent equals fraction numerator 1 over denominator 2 open parentheses 0 close parentheses minus open parentheses 1 close parentheses open parentheses negative 1 close parentheses end fraction open parentheses table row 0 1 row cell negative 1 end cell 2 end table close parentheses  open parentheses A B close parentheses to the power of negative 1 end exponent equals open parentheses table row 0 1 row cell negative 1 end cell 2 end table close parentheses

0

Roboguru

Diketahui matriks . Invers matriks X adalah ...

Pembahasan Soal:

X equals left parenthesis A B right parenthesis  equals open parentheses table row 2 3 row cell negative 1 end cell 1 end table close parentheses open parentheses table row cell negative 3 end cell cell negative 1 end cell row 4 2 end table close parentheses  equals open parentheses table row cell 2 left parenthesis negative 3 right parenthesis plus 3.4 end cell cell 2 left parenthesis negative 1 right parenthesis plus 3 left parenthesis 2 right parenthesis end cell row cell left parenthesis negative 1 right parenthesis left parenthesis negative 3 right parenthesis plus 1.4 end cell cell left parenthesis negative 1 right parenthesis left parenthesis negative 1 right parenthesis plus 1.2 end cell end table close parentheses  equals open parentheses table row cell negative 6 plus 12 end cell cell negative 2 plus 6 end cell row cell 3 plus 4 end cell cell 1 plus 2 end cell end table close parentheses  equals open parentheses table row 6 4 row 7 3 end table close parentheses    X to the power of negative 1 end exponent equals fraction numerator 1 over denominator open vertical bar X close vertical bar end fraction space a d j space X  equals fraction numerator 1 over denominator 6.3 minus 4.7 end fraction open parentheses table row 3 cell negative 4 end cell row cell negative 7 end cell 6 end table close parentheses  equals negative 1 over 10 open parentheses table row 3 cell negative 4 end cell row cell negative 7 end cell 6 end table close parentheses  equals 1 over 10 open parentheses table row cell negative 3 end cell 4 row 7 cell negative 6 end cell end table close parentheses

0

Roboguru

Diketahui matriks   dan . Invers dari matriks BA adalah ..

Pembahasan Soal:

Jawaban E

left parenthesis B A right parenthesis to the power of negative 1 end exponent space equals A to the power of negative 1 end exponent B to the power of negative 1 end exponent

equals open parentheses table row cell negative 2 end cell 0 row 1 7 end table close parentheses open parentheses table row 0 1 row 4 3 end table close parentheses

equals open parentheses table row cell 0 plus 0 end cell cell negative 2 plus 0 end cell row cell 0 plus 28 end cell cell 1 plus 21 end cell end table close parentheses

equals open parentheses table row 0 cell negative 2 end cell row 28 22 end table close parentheses

Jadi invers matriks BA adalah equals open parentheses table row 0 cell negative 2 end cell row 28 22 end table close parentheses

0

Roboguru

Diketahui  dan . Determinan  sama dengan ....

Pembahasan Soal:

Diketahui matriks straight A equals open square brackets table row a b row c d end table close square brackets, maka rumus determinannya adalah:

det space open parentheses straight A close parentheses equals a d minus b c 

Untuk rumus inversnya adalah:

straight A to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open square brackets table row d cell negative b end cell row cell negative c end cell a end table close square brackets  

Hasil dari left parenthesis A B to the power of negative 1 end exponent right parenthesis didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis A B to the power of negative 1 end exponent right parenthesis end cell equals cell open square brackets table row 2 5 row 1 3 end table close square brackets fraction numerator 1 over denominator open parentheses 5 close parentheses open parentheses 1 close parentheses minus open parentheses 4 close parentheses open parentheses 1 close parentheses end fraction open square brackets table row 1 cell negative 4 end cell row cell negative 1 end cell 5 end table close square brackets end cell row blank equals cell open square brackets table row 2 5 row 1 3 end table close square brackets fraction numerator 1 over denominator 5 minus 4 end fraction open square brackets table row 1 cell negative 4 end cell row cell negative 1 end cell 5 end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator 5 minus 4 end fraction open square brackets table row 2 5 row 1 3 end table close square brackets open square brackets table row 1 cell negative 4 end cell row cell negative 1 end cell 5 end table close square brackets end cell row blank equals cell 1 over 1 open square brackets table row 2 5 row 1 3 end table close square brackets open square brackets table row 1 cell negative 4 end cell row cell negative 1 end cell 5 end table close square brackets end cell row blank equals cell open square brackets table row 2 5 row 1 3 end table close square brackets open square brackets table row 1 cell negative 4 end cell row cell negative 1 end cell 5 end table close square brackets end cell row blank equals cell open square brackets table row cell negative 3 end cell 17 row cell negative 2 end cell 11 end table close square brackets end cell end table 

Determinan left parenthesis A B to the power of negative 1 end exponent right parenthesis didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell det space left parenthesis A B to the power of negative 1 end exponent right parenthesis end cell equals cell open parentheses negative 3 close parentheses times open parentheses 11 close parentheses minus open parentheses 17 close parentheses times open parentheses negative 2 close parentheses end cell row blank equals cell negative 33 minus open parentheses negative 34 close parentheses end cell row blank equals cell negative 33 plus 34 end cell row blank equals 1 end table 

Jadi, determinan left parenthesis A B to the power of negative 1 end exponent right parenthesis sama dengan 1.

0

Roboguru

Diketahui matriks  dan , maka

Pembahasan Soal:

Diketahui bahwa, Matriks P equals open parentheses table row 3 cell negative 5 end cell row 4 cell negative 7 end cell end table close parentheses dan Q equals open parentheses table row cell negative 9 end cell 5 row cell negative 7 end cell 4 end table close parentheses, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell P Q end cell equals cell open parentheses table row 3 cell negative 5 end cell row 4 cell negative 7 end cell end table close parentheses open parentheses table row cell negative 9 end cell 5 row cell negative 7 end cell 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 27 plus 35 end cell cell 15 minus 20 end cell row cell negative 36 plus 49 end cell cell 20 minus 28 end cell end table close parentheses end cell row blank equals cell open parentheses table row 8 cell negative 5 end cell row 13 cell negative 8 end cell end table close parentheses end cell end table

Ingat bahwa, invers matriks memiliki rumus fraction numerator 1 over denominator D e t left parenthesis P Q right parenthesis end fraction times open parentheses A d j space P Q close parentheses, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses P Q close parentheses to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator D e t left parenthesis P Q right parenthesis end fraction times open parentheses A d j space P Q close parentheses end cell row blank equals cell fraction numerator 1 over denominator left parenthesis negative 64 plus 65 right parenthesis end fraction open parentheses table row cell negative 8 end cell 5 row cell negative 13 end cell 8 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 8 end cell 5 row cell negative 13 end cell 8 end table close parentheses end cell end table

Jadi, jawaban yang tepat adalah B. 

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved