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Matriks  dan . Jika , dengan  menyatakan transpos matriks , tentukan nilai !

Pertanyaan

Matriks A equals open parentheses table row 5 a row cell 3 b end cell cell 5 c end cell end table close parentheses dan B equals open parentheses table row cell 2 a plus 2 end cell cell a plus 8 end cell row cell a plus 4 end cell cell 3 a minus b end cell end table close parentheses. Jika 2 A equals B to the power of t, dengan B to the power of t menyatakan transpos matriks straight B, tentukan nilai c!

Pembahasan Soal:

Diketahui

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open parentheses table row 5 a row cell 3 b end cell cell 5 c end cell end table close parentheses end cell row B equals cell open parentheses table row cell 2 a plus 2 end cell cell a plus 8 end cell row cell a plus 4 end cell cell 3 a minus b end cell end table close parentheses end cell end table

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 A end cell equals cell B to the power of t end cell row cell 2 open parentheses table row 5 a row cell 3 b end cell cell 5 c end cell end table close parentheses end cell equals cell open parentheses table row cell 2 a plus 2 end cell cell a plus 4 end cell row cell a plus 8 end cell cell 3 a minus b end cell end table close parentheses end cell row cell open parentheses table row 10 cell 2 a end cell row cell 6 b end cell cell 10 c end cell end table close parentheses end cell equals cell open parentheses table row cell 2 a plus 2 end cell cell a plus 4 end cell row cell a plus 8 end cell cell 3 a minus b end cell end table close parentheses end cell end table

Dengan menggunakan konsep kesamaan dua matriks diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a end cell equals cell a plus 4 end cell row cell 2 a minus a end cell equals 4 row a equals 4 end table 

Subtitusikan nilai a untuk menentukan nilai b

 table attributes columnalign right center left columnspacing 0px end attributes row cell 6 b end cell equals cell a plus 8 end cell row cell 6 b end cell equals cell 4 plus 8 end cell row cell 6 b end cell equals 12 row b equals 2 end table 

Subtitusikan nilai a dan b untuk menentukan nilai c

table attributes columnalign right center left columnspacing 0px end attributes row cell 10 c end cell equals cell 3 a minus b end cell row cell 10 c end cell equals cell 3 open parentheses 4 close parentheses minus 2 end cell row cell 10 c end cell equals cell 12 minus 2 end cell row cell 10 c end cell equals 10 row c equals 1 end table

Dengan demikian nilai c adalah 1.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Indah

Mahasiswa/Alumni Universitas Diponegoro

Terakhir diupdate 30 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui matriks dan . JIka dengan adalah transpos matriks Q, nilai  adalah ... .

Pembahasan Soal:

Ingat bahwa:

A equals open square brackets table row a b row c d end table close square brackets rightwards double arrow m A equals open square brackets table row cell m a end cell cell m b end cell row cell m c end cell cell m d end cell end table close square brackets

  A equals open square brackets table row a b row c d end table close square brackets rightwards double arrow A to the power of T equals open square brackets table row a c row b d end table close square brackets

Pertama kita tentukan terlebih dahulu Q to the power of T:

Q equals open parentheses table row cell c minus 1 end cell cell b minus a end cell row cell d minus 2 end cell cell c minus 2 end cell end table close parentheses rightwards double arrow Q to the power of T equals open parentheses table row cell c minus 1 end cell cell d minus 2 end cell row cell b minus a end cell cell c minus 2 end cell end table close parentheses

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row P equals cell 2 Q to the power of T end cell row cell open parentheses table row cell 3 a minus 1 end cell b row cell d minus 1 end cell cell c plus 2 d end cell end table close parentheses end cell equals cell 2 open parentheses table row cell c minus 1 end cell cell d minus 2 end cell row cell b minus a end cell cell c minus 2 end cell end table close parentheses end cell row cell open parentheses table row cell 3 a minus 1 end cell b row cell d minus 1 end cell cell c plus 2 d end cell end table close parentheses end cell equals cell open parentheses table row cell 2 c minus 2 end cell cell 2 d minus 4 end cell row cell 2 b minus 2 a end cell cell 2 c minus 4 end cell end table close parentheses end cell end table 

Sehingga diperoleh persamaan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a minus 1 end cell equals cell 2 c minus 2 end cell row cell 3 a minus 2 c end cell equals cell negative 1.... open parentheses 1 close parentheses end cell row blank blank blank row b equals cell 2 d minus 4..... open parentheses 2 close parentheses end cell row blank blank blank row cell d minus 1 end cell equals cell 2 b minus 2 a end cell row cell d plus 2 a minus 2 b end cell equals cell 1... open parentheses 3 close parentheses end cell row blank blank blank row cell c plus 2 d end cell equals cell 2 c minus 4 end cell row c equals cell 2 d plus 4........ open parentheses 4 close parentheses end cell end table 

Pertama subtitusi persaman 2 ke persamaan 3

table attributes columnalign right center left columnspacing 0px end attributes row cell d plus 2 a minus 2 b end cell equals 1 row cell d plus 2 a minus 2 left parenthesis 2 d minus 4 right parenthesis end cell equals 1 row cell d plus 2 a minus 4 d plus 8 end cell equals 1 row cell 2 a minus 3 d end cell equals cell negative 7.... open parentheses 5 close parentheses end cell end table 

Subtirusi persaman 4 ke persamaan 1

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a minus 2 c end cell equals cell negative 1 end cell row cell 3 a minus 2 open parentheses 2 d plus 4 close parentheses end cell equals cell negative 1 end cell row cell 3 a minus 4 d minus 8 end cell equals cell negative 1 end cell row cell 3 a minus 4 d end cell equals cell 7.... open parentheses 6 close parentheses end cell end table  

Eliminasi persamaan 5 dan 6.

table row cell table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank d end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table end cell row cell table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a minus 4 d end cell equals 7 end table end cell row blank row blank end table table row cell open vertical bar cross times 3 close vertical bar end cell row cell open vertical bar cross times 2 close vertical bar end cell row blank row blank end table table row cell 6 a minus 9 d equals negative 21 end cell row cell 6 a minus 8 d equals 14 end cell row cell negative d equals negative 35 end cell row cell d equals 35 end cell end table minus 

Subtitusi  nilai d ke persmaan 2 dan  5

table attributes columnalign right center left columnspacing 0px end attributes row b equals cell 2 d minus 4 end cell row blank equals cell 2 open parentheses 35 close parentheses minus 4 end cell row blank equals cell 70 minus 4 end cell row blank equals 66 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a minus 3 d end cell equals cell negative 7 end cell row cell 2 a minus 3 open parentheses 35 close parentheses end cell equals cell negative 7 end cell row cell 2 a minus 105 end cell equals cell negative 7 end cell row cell 2 a end cell equals 98 row a equals 49 end table

Subtitusi nilai a ke persmaan 1

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a minus 2 c end cell equals cell negative 1 end cell row cell 3 open parentheses 49 close parentheses minus 2 c end cell equals cell negative 1 end cell row cell 147 minus 2 c end cell equals cell negative 1 end cell row cell negative 2 c end cell equals cell negative 148 end cell row c equals 74 end table

Sehingga nilai

(ab+cd)===4966+74353.234+2.5905.824

Dengan demikian, nilai open parentheses a b plus c d close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 824 end table

Jadi, tidak ada jawaban yang tepat.

0

Roboguru

Diketahui matriks . Jika 4A - B = CT dan CT adalah transpos matriks C, maka 2x + y + z adalah .....

Pembahasan Soal:

begin mathsize 14px style A equals open parentheses table row 2 cell negative y end cell row cell 2 x end cell cell negative 1 end cell end table close parentheses comma space B equals open parentheses table row 6 cell negative 3 y end cell row cell 12 x end cell 1 end table close parentheses comma space C equals open parentheses table row z 8 row 1 cell negative 5 end cell end table close parentheses  4 A minus B equals C to the power of T  4 open parentheses table row 2 cell negative y end cell row cell 2 x end cell cell negative 1 end cell end table close parentheses minus open parentheses table row 6 cell negative 3 y end cell row cell 12 x end cell 1 end table close parentheses equals open parentheses table row z 1 row 8 cell negative 5 end cell end table close parentheses  open parentheses table row 8 cell negative 4 y end cell row cell 8 x end cell cell negative 4 end cell end table close parentheses minus open parentheses table row 6 cell negative 3 y end cell row cell 12 x end cell 1 end table close parentheses equals open parentheses table row z 1 row 8 cell negative 5 end cell end table close parentheses  open parentheses table row 2 cell negative y end cell row cell negative 4 x end cell cell negative 5 end cell end table close parentheses equals open parentheses table row z 1 row 8 cell negative 5 end cell end table close parentheses  minus 4 x equals 8 rightwards arrow x equals negative 2  minus y equals 1 rightwards arrow y equals negative 1  z equals 2    text Sehingga  end text 2 x plus y plus z equals 2 open parentheses negative 2 close parentheses plus open parentheses negative 1 close parentheses plus 2 equals negative 3 end style

0

Roboguru

Diketahui matriks Jika

Pembahasan Soal:

2 A plus B to the power of T equals C D  2 open parentheses table row cell a space space space b end cell row cell 0 space space space 2 end cell end table close parentheses plus open parentheses table row cell 6 space space space minus 8 end cell row cell 1 space space space space 7 end cell end table close parentheses equals open parentheses table row cell 2 space space minus 2 end cell row cell 1 space space space space c end cell end table close parentheses open parentheses table row cell 1 space space space space minus 1 end cell row cell 0 space space space space 2 end cell end table close parentheses  open table attributes columnalign right end attributes row cell table row cell 2 b end cell row 2 end table end cell row blank end table close curly brackets plus open parentheses table row cell 6 space space space minus 8 end cell row cell 1 space space space 7 end cell end table close parentheses equals open parentheses table row cell 2 open parentheses 1 close parentheses minus 2 open parentheses 0 close parentheses space space space space space space space space space 2 open parentheses negative 1 close parentheses minus 2 open parentheses 2 close parentheses end cell row cell 1 open parentheses 1 close parentheses minus plus c open parentheses 0 close parentheses space space space space space space space 1 open parentheses negative 1 close parentheses plus 2 open parentheses c close parentheses space space space space space end cell end table close parentheses  open parentheses table row cell 2 a plus 6 space space space space 2 b minus 8 end cell row cell 1 space space space space space space space space 9 end cell end table close parentheses equals open parentheses table row cell 2 space space space space minus 6 end cell row cell 1 space space space space 2 c minus 1 end cell end table close parentheses    m a k a comma  2 a plus 6 equals 2  2 a equals negative 4  a equals negative 2  d a n space  2 b minus 8 equals negative 6  2 b equals 2  b equals 1  s e r t a space 9 equals 2 c minus 1  10 equals 2 c  5 equals c  j a d i space n i l a i space d a r i space a plus b minus c equals negative 2 plus 1 minus 5 equals negative 6

2

Roboguru

Diketahui matriks . Jika CT adalah transpose matriks C, maka nilai x - 2y yang memenuhi persamaan 3A - B = CT adalah ....

Pembahasan Soal:

begin mathsize 14px style C to the power of T equals open parentheses table row cell space space 0 end cell cell space space 1 end cell row cell negative 4 end cell cell negative 3 end cell end table close parentheses  3 A minus B equals C to the power of T  3 open parentheses table row x 1 row cell negative 1 end cell y end table close parentheses minus open parentheses table row 3 2 row 1 0 end table close parentheses equals open parentheses table row cell space space space 0 end cell cell space space space 1 end cell row cell negative 4 end cell cell negative 3 end cell end table close parentheses  open parentheses table row cell 3 x end cell 3 row cell negative 3 end cell cell 3 y end cell end table close parentheses minus open parentheses table row 3 2 row 1 0 end table close parentheses equals open parentheses table row cell space space space 0 end cell cell space space space 1 end cell row cell negative 4 end cell cell negative 3 end cell end table close parentheses  open parentheses table row cell 3 x minus 3 end cell cell 3 minus 2 end cell row cell negative 3 minus 1 end cell cell 3 y minus 0 end cell end table close parentheses equals open parentheses table row cell space space space 0 end cell cell space space space 1 end cell row cell negative 4 end cell cell negative 3 end cell end table close parentheses  open parentheses table row cell 3 x minus 3 end cell 1 row cell negative 4 end cell cell 3 y end cell end table close parentheses equals open parentheses table row cell space space space 0 end cell cell space space space 1 end cell row cell negative 4 end cell cell negative 3 end cell end table close parentheses  3 x minus 3 equals 0 rightwards arrow x equals 1  3 y equals negative 3 rightwards arrow y equals negative 1  end style

Maka,

begin mathsize 14px style x minus 2 y equals 1 minus 2 open parentheses negative 1 close parentheses equals 1 plus 2 equals 3 end style

0

Roboguru

Diketahui matriks ,  dan  serta  adalah transpose matriks. Jika , maka nilai  sama dengan ...

Pembahasan Soal:

Diketahui straight C equals open parentheses table row cell negative 2 end cell 3 row 2 4 end table close parentheses maka transpose matriks C adalah

straight C to the power of straight T equals open parentheses table row cell negative 2 end cell 2 row 3 4 end table close parentheses

Berdasarkan konsep perkalian skalar dengan matris, serta kesamaan dan penjumlahan matriks maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell A plus B end cell equals cell 2 C to the power of T end cell row cell open parentheses table row p 5 row cell 2 q end cell cell 3 r end cell end table close parentheses plus open parentheses table row 5 cell negative 1 end cell row 3 2 end table close parentheses end cell equals cell 2 open parentheses table row cell negative 2 end cell 2 row 3 4 end table close parentheses end cell row cell open parentheses table row p 5 row cell 2 q end cell cell 3 r end cell end table close parentheses plus open parentheses table row 5 cell negative 1 end cell row 3 2 end table close parentheses end cell equals cell open parentheses table row cell negative 4 end cell 4 row 6 8 end table close parentheses end cell row cell open parentheses table row cell p plus 5 end cell cell 5 minus 1 end cell row cell 2 q plus 3 end cell cell 3 r plus 2 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 4 end cell 4 row 6 8 end table close parentheses end cell row cell open parentheses table row cell p plus 5 end cell 4 row cell 2 q plus 3 end cell cell 3 r plus 2 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 4 end cell 4 row 6 8 end table close parentheses end cell end table

maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell p plus 5 end cell equals cell negative 4 end cell row p equals cell negative 9 end cell row cell 2 q plus 3 end cell equals 6 row cell 2 q end cell equals cell 6 minus 3 end cell row cell 2 q end cell equals 3 row q equals cell 3 over 2 end cell row cell 3 r plus 2 end cell equals 8 row cell 3 r end cell equals cell 8 minus 2 end cell row cell 3 r end cell equals 6 row r equals 2 end table 

Sehingga nilai p plus 2 q plus r:

table attributes columnalign right center left columnspacing 0px end attributes row cell p plus 2 q plus r end cell equals cell negative 9 plus 2 open parentheses 3 over 2 close parentheses plus 2 end cell row blank equals cell negative 9 plus 3 plus 2 end cell row blank equals cell negative 4 end cell end table 

Dengan demikian nilai p plus 2 q plus r sama dengan negative 4.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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

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