Roboguru

Pertanyaan

P adalah matriks berordo 2 cross times 2 yang memenuhi persamaan:

P open parentheses table row 2 4 row cell negative 1 end cell 3 end table close parentheses equals open parentheses table row 5 15 row 8 cell negative 4 end cell end table close parentheses

Tentukan open vertical bar P close vertical bar.

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

 open vertical bar P close vertical bar adalah negative 14.

Pembahasan

Persamaan matriks bentuk X A equals B berlaku:

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

Invers matriks 2 cross times 2 berlaku:

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

Determinan matriks 2 cross times 2 berlaku:

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

Diperoleh penyelesaiannya sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses table row 2 4 row cell negative 1 end cell 3 end table close parentheses end cell equals cell open parentheses table row 5 15 row 8 cell negative 4 end cell end table close parentheses end cell row P equals cell open parentheses table row 5 15 row 8 cell negative 4 end cell end table close parentheses open parentheses table row 2 4 row cell negative 1 end cell 3 end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses table row 5 15 row 8 cell negative 4 end cell end table close parentheses times fraction numerator 1 over denominator 2 open parentheses 3 close parentheses minus 4 open parentheses negative 1 close parentheses end fraction open parentheses table row 3 cell negative 4 end cell row 1 2 end table close parentheses end cell row blank equals cell open parentheses table row 5 15 row 8 cell negative 4 end cell end table close parentheses times fraction numerator 1 over denominator 6 plus 4 end fraction open parentheses table row 3 cell negative 4 end cell row 1 2 end table close parentheses end cell row blank equals cell open parentheses table row 5 15 row 8 cell negative 4 end cell end table close parentheses times 1 over 10 open parentheses table row 3 cell negative 4 end cell row 1 2 end table close parentheses end cell row blank equals cell open parentheses table row 5 15 row 8 cell negative 4 end cell end table close parentheses open parentheses table row cell 1 over 10 times 3 end cell cell 1 over 10 times open parentheses negative 4 close parentheses end cell row cell 1 over 10 times 1 end cell cell 1 over 10 times 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 5 15 row 8 cell negative 4 end cell end table close parentheses open parentheses table row cell 3 over 10 end cell cell negative 4 over 10 end cell row cell 1 over 10 end cell cell 2 over 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 5 open parentheses 3 over 10 close parentheses plus 15 open parentheses 1 over 10 close parentheses end cell cell 5 open parentheses negative 4 over 10 close parentheses plus 15 open parentheses 2 over 10 close parentheses end cell row cell 8 open parentheses 3 over 10 close parentheses plus open parentheses negative 4 close parentheses open parentheses 1 over 10 close parentheses end cell cell 8 open parentheses negative 4 over 10 close parentheses plus open parentheses negative 4 close parentheses open parentheses 2 over 10 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 15 over 10 plus 15 over 10 end cell cell negative 20 over 10 plus 30 over 10 end cell row cell 24 over 10 minus 4 over 10 end cell cell negative 32 over 10 minus 8 over 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 30 over 10 end cell cell 10 over 10 end cell row cell 20 over 10 end cell cell negative 40 over 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 1 row 2 cell negative 4 end cell end table close parentheses end cell end table

Kemudian tentukan determinan dari matriks P.

table attributes columnalign right center left columnspacing 0px end attributes row P equals cell open parentheses table row 3 1 row 2 cell negative 4 end cell end table close parentheses end cell row cell open vertical bar P close vertical bar end cell equals cell open vertical bar table row 3 1 row 2 cell negative 4 end cell end table close vertical bar end cell row blank equals cell 3 open parentheses negative 4 close parentheses minus 1 open parentheses 2 close parentheses end cell row blank equals cell negative 12 minus 2 end cell row blank equals cell negative 14 end cell end table

Dengan demikian, open vertical bar P close vertical bar adalah negative 14.

71

0.0 (0 rating)

Pertanyaan serupa

Matriks X berordo 2×2 yang memenuhi : (20​31​)X=(82​−6−2​) adalah ....

8

0.0

Jawaban terverifikasi

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

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia