Roboguru

Diketahui matriks ,  dan C=[−8−b​a−14​]. Nilai  dan  yang memenuhi  berturut-turut adalah...

Pertanyaan

Diketahui matriks A equals open square brackets table row 4 cell negative 1 end cell row cell negative 2 end cell 7 end table close square bracketsB equals open square brackets table row cell negative 4 end cell 1 row 2 cell negative 7 end cell end table close square brackets dan C=[8ba14]. Nilai a dan b yang memenuhi A plus 3 B equals C berturut-turut adalah...

Pembahasan Soal:

Kesamaan matriks A plus 3 B equals C, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row 4 cell negative 1 end cell row cell negative 2 end cell 7 end table close parentheses plus 3 open parentheses table row cell negative 4 end cell 1 row 2 cell negative 7 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 8 end cell a row cell negative b end cell cell negative 14 end cell end table close parentheses end cell row cell open parentheses table row 4 cell negative 1 end cell row cell negative 2 end cell 7 end table close parentheses plus open parentheses table row cell 3 open parentheses negative 4 close parentheses end cell cell 3 times thin space 1 end cell row cell 3 times thin space 2 end cell cell 3 open parentheses negative 7 close parentheses end cell end table close parentheses end cell equals cell open parentheses table row cell negative 8 end cell a row cell negative b end cell cell negative 14 end cell end table close parentheses end cell row cell open parentheses table row 4 cell negative 1 end cell row cell negative 2 end cell 7 end table close parentheses plus open parentheses table row cell negative 12 end cell 3 row 6 cell negative 21 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 8 end cell a row cell negative b end cell cell negative 14 end cell end table close parentheses end cell row cell open parentheses table row cell 4 plus open parentheses negative 12 close parentheses end cell cell open parentheses negative 1 close parentheses plus 3 end cell row cell open parentheses negative 2 close parentheses plus 6 end cell cell 7 plus open parentheses negative 21 close parentheses end cell end table close parentheses end cell equals cell open parentheses table row cell negative 8 end cell a row cell negative b end cell cell negative 14 end cell end table close parentheses end cell row cell open parentheses table row cell negative 8 end cell 2 row 4 cell negative 14 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 8 end cell a row cell negative b end cell cell negative 14 end cell end table close parentheses end cell row a equals 2 row cell negative b end cell equals 4 row b equals cell negative 4 end cell end table



Jadi, nilai a dan b yang memenuhi A plus 3 B equals C berturut-turut adalah a equals 2 dan b equals negative 4.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 13 September 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika diketahui  dan AB=C+D. nilai a - b=···

Pembahasan Soal:

begin mathsize 14px style straight A equals open parentheses table row cell negative 1 end cell straight a row cell negative 1 end cell 3 end table close parentheses comma space straight B equals open parentheses table row 2 4 row cell negative 1 end cell cell negative 2 end cell end table close parentheses comma space straight C equals open parentheses table row cell negative 6 end cell cell negative 3 end cell row 1 straight b end table close parentheses comma space straight D equals open parentheses table row 2 cell negative 5 end cell row cell negative 6 end cell cell negative 4 end cell end table close parentheses  asterisk times AB equals open parentheses table row cell negative 1 end cell straight a row cell negative 1 end cell 3 end table close parentheses open parentheses table row 2 4 row cell negative 1 end cell cell negative 2 end cell end table close parentheses  space space space space space space equals open parentheses table row cell negative 2 minus straight a end cell cell negative 4 minus 2 straight a end cell row cell negative 2 minus 3 end cell cell negative 4 minus 6 end cell end table close parentheses  space space space space space space equals open parentheses table row cell negative 2 minus straight a end cell cell negative 4 minus 2 straight a end cell row cell negative 5 end cell cell negative 10 end cell end table close parentheses  asterisk times straight C plus straight D equals open parentheses table row cell negative 6 end cell cell negative 3 end cell row 1 straight b end table close parentheses plus open parentheses table row 2 cell negative 5 end cell row cell negative 6 end cell cell negative 4 end cell end table close parentheses  space space space space space space space space space space equals open parentheses table row cell negative 4 end cell cell negative 8 end cell row cell negative 5 end cell cell negative 4 plus straight b end cell end table close parentheses  asterisk times AB equals straight C plus straight D  space open parentheses table row cell negative 2 minus straight a end cell cell negative 4 minus 2 straight a end cell row cell negative 5 end cell cell negative 10 end cell end table close parentheses equals open parentheses table row cell negative 4 end cell cell negative 8 end cell row cell negative 5 end cell cell negative 4 plus straight b end cell end table close parentheses  asterisk times minus space 2 minus space straight a space equals negative 4 space  space space space space space space space space space minus space straight a equals negative 2 space  space space space space space space space space space space space space space straight a space equals 2  asterisk times minus 4 plus straight b equals negative 10  space space space space space space space space space space space straight b equals negative 6  asterisk times straight a minus straight b space equals 2 minus left parenthesis negative 6 right parenthesis  space space space space space space space space space space equals 2 plus 6 equals 8 end style

Roboguru

Nilai  dari persamaan Matriks  adalah...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell begin mathsize 14px style open parentheses table row cell 2 x end cell 4 row 2 x end table close parentheses end style begin mathsize 14px style open parentheses table row 3 y row y cell negative 3 end cell end table close parentheses end style end cell size 14px equals cell begin mathsize 14px style open parentheses table row 0 cell negative 24 end cell row 0 cell negative 12 end cell end table close parentheses end style end cell row cell begin mathsize 14px style open parentheses table row cell 6 x plus 4 y end cell cell 2 x y minus 12 end cell row cell 6 plus x y end cell cell 2 y minus 3 x end cell end table close parentheses end style end cell size 14px equals cell begin mathsize 14px style open parentheses table row 0 cell negative 24 end cell row 0 cell negative 12 end cell end table close parentheses end style end cell end table 

Sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 6 x plus 4 y end cell equals 0 row blank rightwards double arrow cell 2 open parentheses 3 x plus 2 y close parentheses equals 0 end cell row blank rightwards double arrow cell 3 x plus 2 y equals 0 end cell end table end style

Kemudian,

  begin mathsize 14px style table row cell 3 x plus 2 y equals 0 end cell row cell negative 3 x plus 2 y equals negative 12 space space space minus end cell row cell 6 x equals 12 end cell end table space x equals 2 end style 

maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 2 y end cell equals 0 row cell 3 open parentheses 2 close parentheses plus 2 y end cell equals 0 row cell 6 plus 2 y end cell equals 0 row cell 2 y end cell equals cell negative 6 end cell row y equals cell negative 3 end cell end table end style 

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

Roboguru

Nilai  yang memenuhi persamaan matriks  adalah ....

Pembahasan Soal:

Ingat kembali:

  • 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 open parentheses m close parentheses plus b open parentheses o close parentheses end cell cell a open parentheses n close parentheses plus b open parentheses p close parentheses end cell row cell c open parentheses m close parentheses plus d open parentheses o close parentheses end cell cell c open parentheses n close parentheses plus d open parentheses p close parentheses end cell end table close parentheses
  • Jika open parentheses table row a b row c d end table close parentheses equals open parentheses table row m n row o p end table close parentheses, maka a equals mb equals nc equals o, dan d equals p.

Dengan demikian, 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row 5 cell negative 2 end cell row 9 cell negative 4 end cell end table close parentheses open parentheses table row 2 cell negative 1 end cell row a cell a plus b end cell end table close parentheses end cell equals cell open parentheses table row 1 0 row 0 1 end table close parentheses end cell row cell open parentheses table row cell 5 open parentheses 2 close parentheses plus open parentheses negative 2 close parentheses open parentheses a close parentheses end cell cell 5 open parentheses negative 1 close parentheses plus open parentheses negative 2 close parentheses open parentheses a plus b close parentheses end cell row cell 9 open parentheses 2 close parentheses plus open parentheses negative 4 close parentheses open parentheses a close parentheses end cell cell 9 open parentheses negative 1 close parentheses plus open parentheses negative 4 close parentheses open parentheses a plus b close parentheses end cell end table close parentheses end cell equals cell open parentheses table row 1 0 row 0 1 end table close parentheses end cell row cell open parentheses table row cell 10 plus open parentheses negative 2 a close parentheses end cell cell open parentheses negative 5 close parentheses plus open parentheses negative 2 a minus 2 b close parentheses end cell row cell 18 plus open parentheses negative 4 a close parentheses end cell cell open parentheses negative 9 close parentheses plus open parentheses negative 4 a minus 4 b close parentheses end cell end table close parentheses end cell equals cell open parentheses table row 1 0 row 0 1 end table close parentheses end cell row cell open parentheses table row cell 10 minus 2 a end cell cell negative 5 minus 2 a minus 2 b end cell row cell 18 minus 4 a end cell cell negative 9 minus 4 a minus 4 b end cell end table close parentheses end cell equals cell open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table

sehingga diperoleh:

table row cell 10 minus 2 a equals 1 end cell blank cell midline horizontal ellipsis open parentheses 1 close parentheses end cell row cell negative 5 minus 2 a minus 2 b equals 0 end cell blank cell midline horizontal ellipsis open parentheses 2 close parentheses end cell row cell 18 minus 4 a equals 0 end cell blank cell midline horizontal ellipsis open parentheses 3 close parentheses end cell row cell negative 9 minus 4 a minus 4 b equals 1 end cell blank cell midline horizontal ellipsis open parentheses 4 close parentheses end cell end table

Dari open parentheses 3 close parentheses, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell 18 minus 4 a end cell equals 0 row cell negative 4 a end cell equals cell 0 minus 18 end cell row cell negative 4 a end cell equals cell negative 18 end cell row a equals cell fraction numerator negative 18 over denominator negative 4 end fraction end cell row a equals cell 4 comma 5 end cell end table

Hasil yang sama akan diperoleh dari open parentheses 1 close parentheses, yaitu a equals 4 comma 5.

Dengan menyubtitusi a equals 4 comma 5 ke open parentheses 2 close parentheses, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 5 minus 2 open parentheses 4 comma 5 close parentheses minus 2 b end cell equals 0 row cell negative 5 minus 9 minus 2 b end cell equals 0 row cell negative 14 minus 2 b end cell equals 0 row cell negative 2 b end cell equals cell 0 plus 14 end cell row cell negative 2 b end cell equals 14 row b equals cell fraction numerator 14 over denominator negative 2 end fraction end cell row b equals cell negative 7 end cell end table

Hasil yang sama akan diperoleh dari open parentheses 4 close parentheses, yaitu b equals negative 7.

Oleh karena diperoleh a equals 4 comma 5 dan b equals negative 7, maka nilai a minus b adalah 

table attributes columnalign right center left columnspacing 0px end attributes row cell a minus b end cell equals cell 4 comma 5 minus open parentheses negative 7 close parentheses end cell row blank equals cell 4 comma 5 plus 7 end cell row blank equals cell 11 comma 5 end cell end table

Oleh karena itu, jawaban yang benar adalah E.space 

Roboguru

Diketahui  . Jika , maka rasio nilai terhadap  adalah ....

Pembahasan Soal:

Ingat kembali:

  • 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
  • Jika open parentheses table row a b row c d end table close parentheses equals open parentheses table row m n row o p end table close parentheses, maka a equals mb equals nc equals o, dan d equals p

Dengan demikian, 

table attributes columnalign right center left columnspacing 0px end attributes row cell M times A end cell equals N row cell open parentheses table row cell a minus 5 end cell 4 row cell negative 5 end cell 2 end table close parentheses times open parentheses table row 4 cell negative 1 end cell row 2 cell b minus 1 end cell end table close parentheses end cell equals cell open parentheses table row 0 2 row cell negative 16 end cell 5 end table close parentheses end cell row cell open parentheses table row cell open parentheses a minus 5 close parentheses open parentheses 4 close parentheses plus 4 open parentheses 2 close parentheses end cell cell open parentheses a minus 5 close parentheses open parentheses negative 1 close parentheses plus 4 open parentheses b minus 1 close parentheses end cell row cell negative 5 open parentheses 4 close parentheses plus 2 open parentheses 2 close parentheses end cell cell negative 5 open parentheses negative 1 close parentheses plus 2 open parentheses b minus 1 close parentheses end cell end table close parentheses end cell equals cell open parentheses table row 0 2 row cell negative 16 end cell 5 end table close parentheses end cell row cell open parentheses table row cell 4 a minus 20 plus 8 end cell cell negative a plus 5 plus 4 b minus 4 end cell row cell negative 20 plus 4 end cell cell 5 plus 2 b minus 2 end cell end table close parentheses end cell equals cell open parentheses table row 0 2 row cell negative 16 end cell 5 end table close parentheses end cell row cell open parentheses table row cell 4 a minus 12 end cell cell negative a plus 4 b plus 1 end cell row cell negative 16 end cell cell 2 b plus 3 end cell end table close parentheses end cell equals cell open parentheses table row 0 2 row cell negative 16 end cell 5 end table close parentheses end cell end table

sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 a minus 12 end cell equals 0 row cell 4 a end cell equals cell 0 plus 12 end cell row cell 4 a end cell equals 12 row a equals cell 12 over 4 end cell row a equals 3 end table

dan

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 b plus 3 end cell equals 5 row cell 2 b end cell equals cell 5 minus 3 end cell row cell 2 b end cell equals 2 row b equals cell 2 over 2 end cell row b equals 1 end table

Oleh karena a equals 3 dan b equals 1, maka rasio nilai a terhadap b adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a colon b end cell row blank equals cell 3 colon 1 end cell end table

Oleh karena itu, jawaban yang benar adalah E.space 

Roboguru

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 

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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