Roboguru

Diketahui martiks , . Dan matriks . Hasil dari

Pertanyaan

Diketahui martiks straight a equals open parentheses table row 15 25 30 row 45 60 40 row 10 5 20 end table close parenthesesstraight b equals open parentheses table row 9 row 18 row 24 row 30 end table close parentheses. Dan matriks straight c equals open parentheses table row 8 12 18 row 24 30 6 row 16 22 14 end table close parentheses. Hasil dari straight a minus straight c equals 

Pembahasan Soal:

Soal di atas merupakan salah satu operasi hitung matriks yaitu pengurangan. Operasi pengurangan pada dua matriks harus memiliki ordo yang sama.

Penyelesaian dari operasi hitung matriks tersebut adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a minus straight c end cell equals cell open parentheses table row 15 25 30 row 45 60 40 row 10 5 20 end table close parentheses minus open parentheses table row 8 12 18 row 24 30 6 row 16 22 14 end table close parentheses end cell row blank equals cell open parentheses table row cell 15 minus 8 end cell cell 25 minus 12 end cell cell 30 minus 18 end cell row cell 45 minus 24 end cell cell 60 minus 30 end cell cell 40 minus 6 end cell row cell 10 minus 16 end cell cell 5 minus 22 end cell cell 20 minus 14 end cell end table close parentheses end cell row blank equals cell open parentheses table row 7 13 12 row 21 30 34 row cell negative 6 end cell cell negative 17 end cell 6 end table close parentheses end cell end table 


Dengan demikian, hasil dari operasi hitung matriks tersebut adalah  table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 7 13 12 row 21 30 34 row cell negative 6 end cell cell negative 17 end cell 6 end table close parentheses end cell end table yang berordo 3x3.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

D. Nuryani

Mahasiswa/Alumni Universitas Padjadjaran

Terakhir diupdate 01 Mei 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

Jika bilangan real memenuhi persamaan : , maka

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a open parentheses table row 1 row 0 row 1 end table close parentheses minus 2 b open parentheses table attributes columnalign right end attributes row cell negative 1 end cell row 1 row 0 end table close parentheses plus c open parentheses table attributes columnalign right end attributes row 0 row cell negative 1 end cell row 1 end table close parentheses end cell equals cell open parentheses table row 1 row 2 row 1 end table close parentheses end cell row cell open parentheses table row a row 0 row a end table close parentheses minus open parentheses table attributes columnalign right end attributes row cell negative 2 b end cell row cell 2 b end cell row 0 end table close parentheses plus open parentheses table attributes columnalign right end attributes row 0 row cell negative c end cell row c end table close parentheses end cell equals cell open parentheses table row 1 row 2 row 1 end table close parentheses end cell row cell a plus 2 b plus 0 end cell equals 1 row cell 0 minus 2 b minus c end cell equals 2 row cell a minus 0 plus c end cell equals 1 end table end style

Lalu kita eliminasi begin mathsize 14px style a plus 2 b equals 1 end style dengan begin mathsize 14px style negative 2 b minus c equals 2 end style.

begin mathsize 14px style table row cell a plus 2 b equals 1 end cell row cell negative 2 b minus c equals 2 space plus end cell row cell a minus c equals 3 end cell end table end style

Kemudian kita eliminasi begin mathsize 14px style a minus c equals 3 end style dengan begin mathsize 14px style a plus c equals 1 end style.

begin mathsize 14px style table row cell a minus c equals space space space 3 end cell row cell a plus c equals space space space 1 space minus end cell row cell negative 2 c equals space space space 2 end cell row cell c equals negative 1 end cell end table end style

Kita substitusikan nilai begin mathsize 14px style c end style ke salah satu persamaan.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a plus c end cell equals 1 row cell a minus 1 end cell equals 1 row a equals 2 end table end style

Kita substitusikan nilai begin mathsize 14px style a end style ke salah satu persamaan.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a plus 2 b end cell equals 1 row cell 2 plus 2 b end cell equals 1 row cell 2 b end cell equals cell negative 1 end cell row b equals cell negative 1 half end cell end table end style

Sehingga, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a plus b plus c end cell equals cell 2 plus open parentheses negative 1 half close parentheses plus open parentheses negative 1 close parentheses equals 1 half end cell end table end style.

Jadi, jawaban yang tepat adalah B.

0

Roboguru

Given , , and , find the value of  when  b.

Pembahasan Soal:

Selisih dua matriks adalah sebuah matriks baru yang berordo sama, yaitu elemen-elemennya merupakan hasil pegurangan elemen-elemen matriks A dan B.

open parentheses table row a b row c d end table close parentheses minus open parentheses table row k l row m n end table close parentheses equals open parentheses table row cell a minus k end cell cell b minus l end cell row cell c minus m end cell cell d minus n end cell end table close parentheses  

Perkalian matriks M dengan skalar k dituliskan dengan k times M, adalah sebuah matriks yang dibentuk dengan mengalikan masing-masing elemen dari matriks M dengan k.

k. M equals k times open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k times a end cell cell k times b end cell row cell k times c end cell cell k times d end cell end table close parentheses 

Berdasarkan aturan operasi matriks di atas, didapat perhitungan berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 A minus 2 B end cell equals cell 4 C end cell row cell 3 open parentheses table row 2 cell negative 1 end cell row 1 3 end table close parentheses minus 2 open parentheses table row 5 m row p 4 end table close parentheses end cell equals cell 4 open parentheses table row n 6 row 4 t end table close parentheses end cell row cell open parentheses table row 6 cell negative 3 end cell row 3 9 end table close parentheses minus open parentheses table row 10 cell 2 m end cell row cell 2 p end cell 8 end table close parentheses end cell equals cell open parentheses table row cell 4 n end cell 24 row 16 cell 4 t end cell end table close parentheses end cell row cell open parentheses table row cell negative 4 end cell cell negative 3 minus 2 m end cell row cell 3 minus 2 p end cell 1 end table close parentheses end cell equals cell open parentheses table row cell 4 n end cell 24 row 16 cell 4 t end cell end table close parentheses end cell end table    

Dari kesamaan matriks tersebut, diperoleh:

  • elemen baris 1 dan kolom 1: 

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 n end cell equals cell negative 4 end cell row cell fraction numerator 4 n over denominator 4 end fraction end cell equals cell fraction numerator negative 4 over denominator 4 end fraction end cell row cell therefore space n end cell equals cell negative 1 end cell end table 

  • elemen baris 1 dan kolom 2: 

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 3 minus 2 m end cell equals 24 row cell negative 3 minus 2 m plus 3 end cell equals cell 24 plus 3 end cell row cell fraction numerator negative 2 m over denominator negative 2 end fraction end cell equals cell fraction numerator 27 over denominator negative 2 end fraction end cell row cell therefore space m end cell equals cell negative 27 over 2 end cell end table   

  • elemen baris 2 dan kolom 1: 

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 minus 2 p end cell equals 16 row cell 3 minus 2 p minus 3 end cell equals cell 16 minus 3 end cell row cell fraction numerator negative 2 p over denominator negative 2 end fraction end cell equals cell fraction numerator 13 over denominator negative 2 end fraction end cell row cell therefore space p end cell equals cell negative 13 over 2 end cell end table   

  • elemen baris 2 dan kolom 2: t equals 10 

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 t end cell equals 1 row cell fraction numerator 4 t over denominator 4 end fraction end cell equals cell 1 fourth end cell row cell therefore space t end cell equals cell 1 fourth end cell end table

Jadi, nilai m comma space n comma space p comma dan t pada saat begin mathsize 14px style 3 A minus 2 B equals 4 C end style adalah n equals negative 1m equals negative 27 over 2p equals negative 13 over 2, dan t equals 1 fourth.

0

Roboguru

Diketahui , , dan . Tentukan: b.

Pembahasan Soal:

Oleh karena A to the power of 7 equals A squared times A squared times A squared times A, maka dengan menyubtitusi A equals open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses ke A squared terlebih dahulu, 

table attributes columnalign right center left columnspacing 0px end attributes row cell A squared end cell equals cell open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses squared end cell row blank equals cell open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 open parentheses 1 close parentheses plus 2 open parentheses negative 1 close parentheses end cell cell 1 open parentheses 2 close parentheses plus 2 open parentheses negative 1 close parentheses end cell row cell negative 1 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses end cell cell negative 1 open parentheses 2 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 plus open parentheses negative 2 close parentheses end cell cell 2 plus open parentheses negative 2 close parentheses end cell row cell open parentheses negative 1 close parentheses plus 1 end cell cell open parentheses negative 2 close parentheses plus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses subscript blank subscript text      ingat: end text space k open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k a end cell cell k b end cell row cell k c end cell cell k d end cell end table close parentheses end subscript end subscript end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses 1 end cell cell open parentheses negative 1 close parentheses 0 end cell row cell open parentheses negative 1 close parentheses 0 end cell cell open parentheses negative 1 close parentheses 1 end cell end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table 

sehingga diperoleh

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of 7 end cell equals cell A squared times A squared times A squared times A end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript text  ingat:  end text k M equals M k end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript blank subscript table attributes columnalign left end attributes row cell text ingat: end text end cell row cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table end subscript end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript text  ingat:  end text k M equals M k end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript text  ingat:  end text open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript space text ingat:  end text open parentheses table row 1 0 row 0 1 end table close parentheses M equals M end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript text  ingat:  end text k open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k a end cell cell k b end cell row cell k c end cell cell k d end cell end table close parentheses end subscript end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses 1 end cell cell open parentheses negative 1 close parentheses 2 end cell row cell open parentheses negative 1 close parentheses minus 1 end cell cell open parentheses negative 1 close parentheses minus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell cell negative 2 end cell row 1 1 end table close parentheses end cell end table end style

Oleh karena B to the power of 7 equals B squared times B squared times B squared times B, maka dengan menyubtitusi B equals open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses ke B squared terlebih dahulu, 

table attributes columnalign right center left columnspacing 0px end attributes row cell B squared end cell equals cell open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses squared end cell row blank equals cell open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 open parentheses 1 close parentheses plus 1 open parentheses 0 close parentheses end cell cell 1 open parentheses 1 close parentheses plus 1 open parentheses negative 1 close parentheses end cell row cell 0 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses 0 close parentheses end cell cell 0 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 plus 0 end cell cell 1 plus open parentheses negative 1 close parentheses end cell row cell 0 plus 0 end cell cell 0 plus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table 

sehingga diperolah

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell B to the power of 7 end cell equals cell B squared times B squared times B squared times B end cell row blank equals cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses subscript space space text karena  end text open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end subscript end cell row blank equals cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses subscript space space text karena  end text open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end subscript end cell row blank equals cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses subscript space space text karena  end text open parentheses table row 1 0 row 0 1 end table close parentheses M equals M end subscript end cell row blank equals cell open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses end cell end table end style

Oleh karena C to the power of 7 equals C squared times C squared times C squared times C, maka dengan menyubtitusi C equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses ke C squared terlebih dahulu, 

table attributes columnalign right center left columnspacing 0px end attributes row cell C squared end cell equals cell open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses squared end cell row blank equals cell open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row cell 0 open parentheses 0 close parentheses plus 1 open parentheses negative 1 close parentheses end cell cell 0 open parentheses 1 close parentheses plus 1 open parentheses 0 close parentheses end cell row cell open parentheses negative 1 close parentheses open parentheses 0 close parentheses plus 0 open parentheses negative 1 close parentheses end cell cell open parentheses negative 1 close parentheses open parentheses 1 close parentheses plus 0 open parentheses 0 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 0 plus open parentheses negative 1 close parentheses end cell cell 0 plus 0 end cell row cell 0 plus 0 end cell cell open parentheses negative 1 close parentheses plus 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses subscript text      ingat: end text space k open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k a end cell cell k b end cell row cell k c end cell cell k d end cell end table close parentheses end subscript end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses 1 end cell cell open parentheses negative 1 close parentheses 0 end cell row cell open parentheses negative 1 close parentheses 0 end cell cell open parentheses negative 1 close parentheses 1 end cell end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table 

sehingga diperoleh

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell C to the power of 7 end cell equals cell C squared times C squared times C squared times C end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript text  ingat:  end text k M equals M k end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript blank subscript table attributes columnalign left end attributes row cell text ingat: end text end cell row cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table end subscript end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript text  ingat:  end text k M equals M k end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript text  ingat:  end text open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript space text ingat:  end text open parentheses table row 1 0 row 0 1 end table close parentheses M equals M end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript text  ingat:  end text k open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k a end cell cell k b end cell row cell k c end cell cell k d end cell end table close parentheses end subscript end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses 0 end cell cell open parentheses negative 1 close parentheses 1 end cell row cell open parentheses negative 1 close parentheses minus 1 end cell cell open parentheses negative 1 close parentheses 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses end cell end table end style

Dengan demikian, 

table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of 7 plus B to the power of 7 minus C to the power of 7 end cell equals cell open parentheses table row cell negative 1 end cell cell negative 2 end cell row 1 1 end table close parentheses plus open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses minus open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 plus 1 minus 0 end cell cell negative 2 plus 1 minus open parentheses negative 1 close parentheses end cell row cell 1 plus 0 minus 1 end cell cell 1 plus open parentheses negative 1 close parentheses minus 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 0 row 0 0 end table close parentheses end cell end tablespace 

0

Roboguru

Diketahui matriks ,  dan . Jika  maka  adalah ....

Pembahasan Soal:

Operasi pengurangan pada matriks :

table attributes columnalign right center left columnspacing 0px end attributes row cell straight A minus straight B end cell equals cell open parentheses table row 4 cell negative 9 end cell row 3 cell negative 4 straight p end cell end table close parentheses minus open parentheses table row cell 5 straight p end cell cell negative 5 end cell row 1 3 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus 5 straight p end cell cell negative 9 plus 5 end cell row cell 3 minus 1 end cell cell negative 4 straight p minus 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus 5 straight p end cell cell negative 4 end cell row 2 cell negative 4 straight p minus 3 end cell end table close parentheses end cell end table 

Invers matriks C.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight C to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator det space straight C end fraction Adj space straight C end cell row blank equals cell fraction numerator 1 over denominator left parenthesis negative 10 right parenthesis times 6 straight p minus left parenthesis negative 4 right parenthesis times left parenthesis 8 right parenthesis end fraction open parentheses table row cell 6 straight p end cell cell negative 8 end cell row 4 cell negative 10 end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 60 straight p plus 32 end fraction open parentheses table row cell 6 straight p end cell cell negative 8 end cell row 4 cell negative 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 6 straight p over denominator negative 60 straight p plus 32 end fraction end cell cell fraction numerator negative 8 over denominator negative 60 straight p plus 32 end fraction end cell row cell fraction numerator 4 over denominator negative 60 straight p plus 32 end fraction end cell cell fraction numerator negative 10 over denominator negative 60 straight p plus 32 end fraction end cell end table close parentheses end cell end table 

Kesamaan matriks A minus B equals C to the power of negative 1 end exponent comma maka :

open parentheses table row cell 4 minus 5 straight p end cell cell negative 4 end cell row 2 cell negative 4 straight p minus 3 end cell end table close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell fraction numerator 6 straight p over denominator negative 60 straight p plus 32 end fraction end cell cell fraction numerator negative 8 over denominator negative 60 straight p plus 32 end fraction end cell row cell fraction numerator 4 over denominator negative 60 straight p plus 32 end fraction end cell cell fraction numerator negative 10 over denominator negative 60 straight p plus 32 end fraction end cell end table close parentheses end cell end table

Dari hasiil di ayas maka:

table attributes columnalign right center left columnspacing 0px end attributes row 2 equals cell fraction numerator 4 over denominator negative 60 straight p plus 32 end fraction end cell row cell 2 left parenthesis negative 60 straight p plus 32 right parenthesis end cell equals 4 row cell negative 120 straight p plus 64 end cell equals 4 row cell negative 120 straight p end cell equals cell negative 60 end cell row straight p equals cell fraction numerator negative 60 over denominator negative 120 end fraction end cell row blank equals cell 1 half end cell row cell 2 straight p end cell equals 1 end table 

Jadii, nilia  2 p adalah 1.

1

Roboguru

Temukan hasil dari operasi antarmatriks berikut ini jika ada. e.

Pembahasan Soal:

Selisih dua matriks adalah sebuah matriks baru yang berordo sama, yaitu elemen-elemennya merupakan hasil pengurangan elemen-elemen matriks A dan B.

open parentheses table row a b row c d end table close parentheses minus open parentheses table row k l row m n end table close parentheses equals open parentheses table row cell a minus k end cell cell b minus l end cell row cell c minus m end cell cell d minus n end cell end table close parentheses  

Dua buah matriks hanya dapat dikurangkan apabila kedua matriks itu berordo sama.

   table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row 1 0 0 row 0 1 0 row 0 0 1 end table close parentheses minus open parentheses table row 1 7 2 row 4 5 6 row 1 5 6 end table close parentheses end cell equals cell open parentheses table row cell 1 minus 1 end cell cell 0 minus 7 end cell cell 0 minus 2 end cell row cell 0 minus 4 end cell cell 1 minus 5 end cell cell 0 minus 6 end cell row cell 0 minus 1 end cell cell 0 minus 5 end cell cell 1 minus 6 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 cell negative 7 end cell cell negative 2 end cell row cell negative 4 end cell cell negative 4 end cell cell negative 6 end cell row cell negative 1 end cell cell negative 5 end cell cell negative 5 end cell end table close parentheses end cell end table   

Jadi, hasil dari operasi antarmatriks tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 0 cell negative 7 end cell cell negative 2 end cell row cell negative 4 end cell cell negative 4 end cell cell negative 6 end cell row cell negative 1 end cell cell negative 5 end cell cell negative 5 end cell end table close parentheses end cell end table.

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