Roboguru

Diketahui A=(12​−12​) dan B=(10​−14​). Jika C adalah matriks berordo 2×2, sehingga C⋅A=B, maka  adalah matriks ....

Pertanyaan

Diketahui A equals open parentheses table row 1 cell negative 1 end cell row 2 2 end table close parentheses dan B equals open parentheses table row 1 cell negative 1 end cell row 0 4 end table close parentheses. Jika C adalah matriks berordo 2 cross times 2, sehingga C times A equals B, maka C adalah matriks ....

  1. open parentheses table row 1 0 row cell negative 1 end cell 2 end table close parentheses 

  2. open parentheses table row 1 0 row 1 cell negative 2 end cell end table close parentheses 

  3. open parentheses table row 1 0 row 2 1 end table close parentheses 

  4. open parentheses table row 1 0 row cell negative 2 end cell 1 end table close parentheses 

  5. open parentheses table row 1 0 row cell negative 1 end cell 2 end table close parentheses 

Pembahasan Video:

Pembahasan Soal:

Ingat bahwa:

Sifat invers matriks : X times A equals B left right double arrow X equals B times A to the power of negative 1 end exponent. Sehingga C times A equals B left right double arrow C equals B times A to the power of negative 1 end exponent.

Langkah pertama carilah invers dari matriks A.

table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator open vertical bar A close vertical bar end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator 1 times 2 minus left parenthesis negative 1 right parenthesis times 2 end fraction open parentheses table row 2 1 row cell negative 2 end cell 1 end table close parentheses end cell row blank equals cell 1 fourth open parentheses table row 2 1 row cell negative 2 end cell 1 end table close parentheses end cell end table

Jadi, invers matriks A adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth open parentheses table row 2 1 row cell negative 2 end cell 1 end table close parentheses end cell end table.

Langkah kedua kalikan matriks B dengan invers dari matriks A, maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row C equals cell open parentheses table row 1 cell negative 1 end cell row 0 4 end table close parentheses 1 fourth open parentheses table row 2 1 row cell negative 2 end cell 1 end table close parentheses end cell row blank equals cell 1 fourth open parentheses table row 1 cell negative 1 end cell row 0 4 end table close parentheses open parentheses table row 2 1 row cell negative 2 end cell 1 end table close parentheses end cell row blank equals cell 1 fourth open parentheses table row 4 0 row cell negative 8 end cell 4 end table close parentheses end cell row blank equals cell open parentheses table row 1 0 row cell negative 2 end cell 1 end table close parentheses end cell end table

Sehingga diperoleh, matriks C yang memenuhi persamaan C times A equals B adalah open parentheses table row 1 0 row cell negative 2 end cell 1 end table close parentheses.

Oleh karena itu, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 07 Oktober 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

Perhatikan matriks-matriks berikut. A=(6−5​73​), C=(0−2​84​), dan D=(2−7​4731​). Jika D=A+BC, matriks B=. . . .

Pembahasan Soal:

  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row C equals cell open parentheses table row 0 8 row cell negative 2 end cell 4 end table close parentheses end cell row cell C to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator 0 cross times 4 minus 8 cross times open parentheses negative 2 close parentheses end fraction open parentheses table row 4 cell negative 8 end cell row 2 0 end table close parentheses end cell row blank equals cell 1 over 16 open parentheses table row 4 cell negative 8 end cell row 2 0 end table close parentheses end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row D equals cell A plus B C end cell row cell D minus A end cell equals cell B C end cell row cell open parentheses D minus A close parentheses C to the power of negative 1 end exponent end cell equals B row space left right double arrow cell space B equals left parenthesis D minus A right parenthesis C to the power of negative 1 end exponent end cell row B equals cell open square brackets open parentheses table row 2 47 row cell negative 7 end cell 31 end table close parentheses minus open parentheses table row 6 7 row cell negative 5 end cell 3 end table close parentheses close square brackets 1 over 16 open parentheses table row 4 cell negative 8 end cell row 2 0 end table close parentheses end cell row B equals cell 1 over 16 open parentheses table row cell negative 4 end cell 40 row cell negative 2 end cell 28 end table close parentheses open parentheses table row 4 cell negative 8 end cell row 2 0 end table close parentheses end cell row B equals cell 1 over 16 open parentheses table row cell open parentheses negative 4 close parentheses open parentheses 4 close parentheses plus open parentheses 40 close parentheses open parentheses 2 close parentheses end cell cell left parenthesis negative 4 right parenthesis left parenthesis negative 8 right parenthesis plus left parenthesis 40 right parenthesis left parenthesis 0 right parenthesis end cell row cell left parenthesis negative 2 right parenthesis left parenthesis 4 right parenthesis plus left parenthesis 28 right parenthesis left parenthesis 2 right parenthesis end cell cell left parenthesis negative 2 right parenthesis left parenthesis negative 8 right parenthesis plus left parenthesis 28 right parenthesis left parenthesis 0 right parenthesis end cell end table close parentheses end cell row B equals cell 1 over 16 open parentheses table row 64 32 row 48 16 end table close parentheses end cell row B equals cell open parentheses table row 4 2 row 3 1 end table close parentheses end cell end table end style

Jadi, tidak ada jawaban yang tepat.

 

3

Roboguru

Diketahui matriksA=(−21​−3−1​), B=(010​−5−5​), dan XA=B, matriks X adalah...

Pembahasan Soal:

Ingat bahwa:

A=(acbd)A1=adcb1(dcba)

X times A equals B rightwards arrow X equals B times A to the power of negative 1 end exponent

Pertama kita menetukan A to the power of negative 1 end exponent , sehingga:

A1===2×(1)(3)×11(1132)2+31(1132)51(1132) 

Sehingga diperoleh perhitungan:

 X======BA1(01055)51(1132)51(01055)(1132)51(0+510+50+1030+10)51(551040)(1128) 

Dengan demikian. matriks X adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 1 2 row cell negative 1 end cell 8 end table close parentheses end cell end table

Jadi, jawaban yang tepat adalah C

0

Roboguru

Jika A matriks berordo 2×2 sehingga A(1−1​)=(−15​) dan A(21​)=(47​), maka A2= ...

Pembahasan Soal:

Misal: P adalah matriks table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 1 2 row cell negative 1 end cell 1 end table close parentheses end cell end table dan Q adalah matriks open parentheses table row cell negative 1 end cell 4 row 5 7 end table close parentheses.

Sehingga pada soal terbentuk operasi matriks A P equals Q.

Dengan menggunakan sifat invers matriks, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell A P end cell equals Q row A equals cell Q P to the power of negative 1 end exponent end cell end table

Sehingga diperoleh penyelesaiannya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell Q P to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row cell negative 1 end cell 4 row 5 7 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell 1 end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row cell negative 1 end cell 4 row 5 7 end table close parentheses times fraction numerator 1 over denominator 1 open parentheses 1 close parentheses minus 2 open parentheses negative 1 close parentheses end fraction open parentheses table row 1 cell negative 2 end cell row 1 1 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 4 row 5 7 end table close parentheses times fraction numerator 1 over denominator 1 plus 2 end fraction open parentheses table row 1 cell negative 2 end cell row 1 1 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 4 row 5 7 end table close parentheses times 1 third open parentheses table row 1 cell negative 2 end cell row 1 1 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 4 row 5 7 end table close parentheses times open parentheses table row cell 1 third open parentheses 1 close parentheses end cell cell 1 third open parentheses negative 2 close parentheses end cell row cell 1 third open parentheses 1 close parentheses end cell cell 1 third open parentheses 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 4 row 5 7 end table close parentheses times open parentheses table row cell 1 third end cell cell negative 2 over 3 end cell row cell 1 third end cell cell 1 third end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 open parentheses 1 third close parentheses plus 4 open parentheses 1 third close parentheses end cell cell negative 1 open parentheses negative 2 over 3 close parentheses plus 4 open parentheses 1 third close parentheses end cell row cell 5 open parentheses 1 third close parentheses plus 7 open parentheses 1 third close parentheses end cell cell 5 open parentheses negative 2 over 3 close parentheses plus 7 open parentheses 1 third close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 third plus 4 over 3 end cell cell 2 over 3 plus 4 over 3 end cell row cell 5 over 3 plus 7 over 3 end cell cell negative 10 over 3 plus 7 over 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 3 over 3 end cell cell 6 over 3 end cell row cell 12 over 3 end cell cell negative 3 over 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 2 row 4 cell negative 1 end cell end table close parentheses end cell end table

Diperoleh matriks A equals open parentheses table row 1 2 row 4 cell negative 1 end cell end table close parentheses.

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row A equals cell open parentheses table row 1 2 row 4 cell negative 1 end cell end table close parentheses end cell row cell A squared end cell equals cell open parentheses table row 1 2 row 4 cell negative 1 end cell end table close parentheses open parentheses table row 1 2 row 4 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 4 close parentheses end cell cell 1 open parentheses 2 close parentheses plus 2 open parentheses negative 1 close parentheses end cell row cell 4 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses 4 close parentheses end cell cell 4 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 8 end cell cell 2 minus 2 end cell row cell 4 minus 4 end cell cell 8 plus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 9 0 row 0 9 end table close parentheses end cell end table

Maka A squared equalsopen parentheses table row 9 0 row 0 9 end table close parentheses.

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Tentukan nilai matriks X yang memenuhi persamaan berikut: a. X(6−1​−51​)=(34​−27​)

Pembahasan Soal:

Ingat kembai:

- Determinan Matriks

A equals open parentheses table row straight a straight b row straight c straight d end table close parentheses rightwards arrow det. space A equals ad minus bc 

- Invers Matriks

A equals open parentheses table row straight a straight b row straight c straight d end table close parentheses rightwards arrow A to the power of negative 1 end exponent equals fraction numerator 1 over denominator det. space A end fraction open parentheses table row straight d cell negative straight b end cell row cell negative straight c end cell straight a end table close parentheses 

- Sifat-sifat Invers Matriks

A X equals B rightwards arrow X equals A to the power of negative 1 end exponent times B X A equals B rightwards arrow X equals B times A to the power of negative 1 end exponent 

Maka:

X(6151)XXXXXXX========(3427)(3427)(6151)1(3427)61(5)(1)1(1156)(3427)651(1156)(3427)11(1156)(3427)(1156)(324+7151220+42)(111362) 

Jadi, nilai matriks X yang memenuhi persamaan tersebut adalah (111362).

0

Roboguru

Jika x(−611​7−9​)=(45​3−2​), maka x=...

Pembahasan Soal:

Ingat jika X times A equals B maka X equals B times A to the power of negative 1 end exponent 

Perhatikan perhitungan berikut 

table attributes columnalign right center left columnspacing 0px end attributes row cell x open parentheses table row cell negative 6 end cell 7 row 11 cell negative 9 end cell end table close parentheses end cell equals cell open parentheses table row 4 3 row 5 cell negative 2 end cell end table close parentheses end cell row X equals cell open parentheses table row 4 3 row 5 cell negative 2 end cell end table close parentheses times open parentheses table row cell negative 6 end cell 7 row 11 cell negative 9 end cell end table close parentheses to the power of negative 1 end exponent end cell row X equals cell open parentheses table row 4 3 row 5 cell negative 2 end cell end table close parentheses open parentheses fraction numerator 1 over denominator open parentheses negative 6 close parentheses open parentheses negative 9 close parentheses minus open parentheses 11 close parentheses open parentheses 7 close parentheses end fraction times open parentheses table row cell negative 9 end cell cell negative 7 end cell row cell negative 11 end cell cell negative 6 end cell end table close parentheses close parentheses end cell row X equals cell open parentheses table row 4 3 row 5 cell negative 2 end cell end table close parentheses open parentheses fraction numerator 1 over denominator 54 minus 77 end fraction times open parentheses table row cell negative 9 end cell cell negative 7 end cell row cell negative 11 end cell cell negative 6 end cell end table close parentheses close parentheses end cell row X equals cell open parentheses table row 4 3 row 5 cell negative 2 end cell end table close parentheses open parentheses fraction numerator 1 over denominator 54 minus 77 end fraction times open parentheses table row cell negative 9 end cell cell negative 7 end cell row cell negative 11 end cell cell negative 6 end cell end table close parentheses close parentheses end cell row X equals cell open parentheses table row 4 3 row 5 cell negative 2 end cell end table close parentheses open parentheses fraction numerator 1 over denominator negative 23 end fraction times open parentheses table row cell negative 9 end cell cell negative 7 end cell row cell negative 11 end cell cell negative 6 end cell end table close parentheses close parentheses end cell row X equals cell fraction numerator 1 over denominator negative 23 end fraction times open parentheses table row 4 3 row 5 cell negative 2 end cell end table close parentheses times open parentheses table row cell negative 9 end cell cell negative 7 end cell row cell negative 11 end cell cell negative 6 end cell end table close parentheses end cell row X equals cell negative 1 over 23 times open parentheses table row cell negative 36 minus 33 end cell cell negative 28 minus 18 end cell row cell negative 45 plus 22 end cell cell negative 35 plus 12 end cell end table close parentheses end cell row X equals cell negative 1 over 23 times open parentheses table row cell negative 69 end cell cell negative 46 end cell row cell negative 23 end cell cell negative 23 end cell end table close parentheses end cell row X equals cell open parentheses table row 3 2 row 1 1 end table close parentheses end cell end table 

Dengan demikian, jawaban yang tepat adalah C.

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