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Pertanyaan

Hasil dari begin mathsize 14px style open square brackets table row 2 1 row 7 3 end table close square brackets open square brackets table row 8 6 row 1 5 end table close square brackets equals.... end style 

 

Pembahasan Soal:

Perkalian Dua 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 h b end cell row cell c e plus d g end cell cell c f plus d h end cell end table close square brackets 

table attributes columnalign right center left columnspacing 0px end attributes row cell open square brackets table row 2 1 row 7 3 end table close square brackets open square brackets table row 8 6 row 1 5 end table close square brackets end cell equals cell open square brackets table row cell 2 times 8 plus 1 times 1 end cell cell 2 times 6 plus 1 times 5 end cell row cell 7 times 8 plus 3 times 1 end cell cell 7 times 6 plus 3 times 5 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 16 plus 1 end cell cell 12 plus 5 end cell row cell 56 plus 3 end cell cell 42 plus 15 end cell end table close square brackets end cell row blank equals cell open square brackets table row 17 17 row 59 57 end table close square brackets end cell end table 

Jadi, hasil dari open square brackets table row 2 1 row 7 3 end table close square brackets open square brackets table row 8 6 row 1 5 end table close square brackets adalah open square brackets table row 17 17 row 59 57 end table close square brackets.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Mustikowati

Mahasiswa/Alumni Universitas Negeri Jakarta

Terakhir diupdate 01 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diberikan matriks A dan B berordo  dengan . Matriks

Pembahasan Soal:

Ingat kembali: Jika matriks A equals open parentheses table row a b row c d end table close parentheses dan B equals open parentheses table row m n row o p end table close parentheses, maka

  • A B equals open parentheses table row a b row c d end table close parentheses open parentheses table row m n row o p end table close parentheses equals open parentheses table row cell a m plus b o end cell cell a n plus b p end cell row cell c m plus d o end cell cell c n plus d p end cell end table close parentheses
  • table attributes columnalign right center left columnspacing 0px end attributes row cell A squared plus A B plus B A plus B squared end cell equals cell open parentheses A plus B close parentheses open parentheses A plus B close parentheses end cell end table
  • A plus B equals B plus A

Dengan demikian, 

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell A squared plus A B plus B A plus B squared end cell equals cell open parentheses A plus B close parentheses open parentheses A plus B close parentheses end cell row cell A squared plus B squared plus A B plus B A end cell equals cell open parentheses A plus B close parentheses open parentheses A plus B close parentheses end cell row cell A squared plus B squared plus open parentheses table row cell negative 12 end cell 0 row 12 0 end table close parentheses end cell equals cell open parentheses table row 0 1 row cell negative 4 end cell cell negative 3 end cell end table close parentheses open parentheses table row 0 1 row cell negative 4 end cell cell negative 3 end cell end table close parentheses end cell row cell A squared plus B squared plus open parentheses table row cell negative 12 end cell 0 row 12 0 end table close parentheses end cell equals cell open parentheses table row cell 0 open parentheses 0 close parentheses plus 1 open parentheses negative 4 close parentheses end cell cell 0 open parentheses 1 close parentheses plus 1 open parentheses negative 3 close parentheses end cell row cell open parentheses negative 4 close parentheses open parentheses 0 close parentheses plus open parentheses negative 3 close parentheses open parentheses negative 4 close parentheses end cell cell open parentheses negative 4 close parentheses open parentheses 1 close parentheses plus open parentheses negative 3 close parentheses open parentheses negative 3 close parentheses end cell end table close parentheses end cell row cell A squared plus B squared plus open parentheses table row cell negative 12 end cell 0 row 12 0 end table close parentheses end cell equals cell open parentheses table row cell 0 plus open parentheses negative 4 close parentheses end cell cell 0 plus open parentheses negative 3 close parentheses end cell row cell 0 plus 12 end cell cell open parentheses negative 4 close parentheses plus 9 end cell end table close parentheses end cell row cell A squared plus B squared plus open parentheses table row cell negative 12 end cell 0 row 12 0 end table close parentheses end cell equals cell open parentheses table row cell negative 4 end cell cell negative 3 end cell row 12 5 end table close parentheses end cell row cell A squared plus B squared end cell equals cell open parentheses table row cell negative 4 end cell cell negative 3 end cell row 12 5 end table close parentheses minus open parentheses table row cell negative 12 end cell 0 row 12 0 end table close parentheses end cell row cell A squared plus B squared end cell equals cell open parentheses table row cell negative 4 minus open parentheses negative 12 close parentheses end cell cell negative 3 minus 0 end cell row cell 12 minus 12 end cell cell 5 minus 0 end cell end table close parentheses end cell row cell A squared plus B squared end cell equals cell open parentheses table row 8 cell negative 3 end cell row 0 5 end table close parentheses end cell end table end style

Jadi, matriks A squared plus B squared equals open parentheses table row 8 cell negative 3 end cell row 0 5 end table close parentheses.

Oleh karena itu, jawaban yang benar adalah A.space 

2

Roboguru

Jika matrik  dan , maka 2PQ = ....

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 PQ end cell equals cell 2 cross times open square brackets table row cell negative 2 end cell 1 end table close square brackets cross times open square brackets table row 1 3 row 4 cell negative 1 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 4 end cell 2 end table close square brackets cross times open square brackets table row 1 3 row 4 cell negative 1 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 4 cross times 1 plus 2 cross times 3 end cell row cell negative 4 cross times 4 plus 2 cross times negative 1 end cell end table close square brackets end cell row blank equals cell open square brackets table row 2 row cell negative 18 end cell end table close square brackets end cell end table

Jadi, nilai dari matrik 2 PQ equals open square brackets table row 2 row cell negative 18 end cell end table close square brackets.

0

Roboguru

diketahui persamaan nilai a+b+c+d =...

Pembahasan Soal:

open parentheses table row a 4 row cell negative 1 end cell c end table close parentheses plus open parentheses table row 2 b row d cell negative 3 end cell end table close parentheses equals open parentheses table row 1 cell negative 3 end cell row 3 4 end table close parentheses open parentheses table row 0 1 row 1 0 end table close parentheses

open parentheses table row cell a plus 2 end cell cell 4 plus b end cell row cell negative 1 plus d end cell cell c minus 3 end cell end table close parentheses equals open parentheses table row cell negative 3 end cell 1 row 4 3 end table close parentheses

Maka,

a+2=-3

a=-5

 

4+b=1

b=-3

 

c-3=3

c=6

 

-1+d=4

d=5

Jadi a+b+c+d=-5-3+6+5=3

Jawaban D

0

Roboguru

Jika diketahui , maka ...

Pembahasan Soal:

Diketahui kesamaan matriks,

open parentheses table row m n row 2 3 end table close parentheses open parentheses table row 1 2 row 4 3 end table close parentheses equals open parentheses table row 24 23 row 14 13 end table close parentheses

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row m n row 2 3 end table close parentheses open parentheses table row 1 2 row 4 3 end table close parentheses end cell equals cell open parentheses table row 24 23 row 14 13 end table close parentheses end cell row cell open parentheses table row cell m times 1 plus n times 4 end cell cell m times 2 plus n times 3 end cell row cell 2 times 1 plus times 3 times 4 end cell cell 2 times 2 plus 3 times 3 end cell end table close parentheses end cell equals cell open parentheses table row 24 23 row 14 13 end table close parentheses end cell row cell open parentheses table row cell m plus 4 n end cell cell 2 m plus 3 n end cell row cell 2 plus 12 end cell cell 4 plus 9 end cell end table close parentheses end cell equals cell open parentheses table row 24 23 row 14 13 end table close parentheses end cell row cell open parentheses table row cell m plus 4 n end cell cell 2 m plus 3 n end cell row 14 13 end table close parentheses end cell equals cell open parentheses table row 24 23 row 14 13 end table close parentheses end cell row blank blank blank end table

Di dapatkan persamaan m plus 4 n equals 24 dan 2 m plus 3 n equals 23. Eliminasi kedua persamaan untuk mencari nilai m dan n.

table attributes columnalign right center left columnspacing 0px end attributes row cell m plus 4 n end cell equals cell 24 rightwards arrow dikali space 2 end cell row cell 2 m plus 3 n end cell equals 23 row blank blank blank row blank blank cell fraction numerator 2 m plus 8 n equals 48 2 m plus 3 n equals 23 minus over denominator 5 n equals 25 end fraction end cell row n equals cell 25 divided by 5 end cell row n equals 5 row blank blank blank row cell 2 m plus 3 n end cell equals 23 row cell 2 m plus 3 left parenthesis 5 right parenthesis end cell equals 23 row cell 2 m plus 15 end cell equals 23 row cell 2 m end cell equals cell 23 minus 15 end cell row cell 2 m end cell equals 8 row m equals cell 8 divided by 2 end cell row m equals 4 end table

Di dapatkan m equals 4 dan n equals 5. Maka,

m space colon thin space n space equals space 4 space colon space 5.
 

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Selesaikan dan tulis dalam bentuk paling sederhana. a.

Pembahasan Soal:

Diketahui:

begin mathsize 14px style open parentheses table row 0 b row c cell d minus a end cell end table close parentheses open parentheses table row cell a minus d end cell b row c 0 end table close parentheses end style

Ditanya:

Bentuk paling sederhana dari begin mathsize 14px style open parentheses table row 0 b row c cell d minus a end cell end table close parentheses open parentheses table row cell a minus d end cell b row c 0 end table close parentheses end style

Perkalian matriks merupakan suatu nilai matriks yang bisa dihasilkan dengan cara tiap baris dikalikan dengan setiap kolom yang jumlah pada barisnya sama.

Bentuk sederhana dari begin mathsize 14px style open parentheses table row 0 b row c cell d minus a end cell end table close parentheses open parentheses table row cell a minus d end cell b row c 0 end table close parentheses end style:

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

Jadi, bentuk paling sederhana dari begin mathsize 14px style open parentheses table row 0 b row c cell d minus a end cell end table close parentheses open parentheses table row cell a minus d end cell b row c 0 end table close parentheses end style adalah open parentheses table row cell b c end cell 0 row 0 cell c b end cell end table close parentheses.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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