Roboguru
SD
SMP
SMA
UTBK/SNBT

Iklan

Iklan

Pertanyaan

Invers dari matriks adalah ....

Invers dari matriks begin mathsize 14px style A equals open parentheses table row 2 cell negative 1 end cell 5 row 1 1 0 row 2 cell negative 3 end cell 2 end table close parentheses end style adalah ....

  1. begin mathsize 14px style negative 1 over 19 open parentheses table row cell negative 2 end cell 13 5 row 2 6 cell negative 5 end cell row 5 cell negative 4 end cell cell negative 3 end cell end table close parentheses end style 

  2. begin mathsize 14px style negative 1 over 19 open parentheses table row 2 cell negative 2 end cell cell negative 5 end cell row cell negative 13 end cell cell negative 6 end cell 4 row cell negative 5 end cell 5 3 end table close parentheses end style 

  3. begin mathsize 14px style negative 1 over 19 open parentheses table row 2 cell negative 13 end cell cell negative 5 end cell row cell negative 2 end cell cell negative 6 end cell 5 row cell negative 5 end cell 4 3 end table close parentheses end style 

  4. begin mathsize 14px style 1 over 19 open parentheses table row 2 cell negative 13 end cell cell negative 5 end cell row cell negative 2 end cell cell negative 6 end cell 5 row cell negative 5 end cell 4 3 end table close parentheses end style 

  5. begin mathsize 14px style 1 over 19 open parentheses table row 2 cell negative 2 end cell cell negative 5 end cell row cell negative 13 end cell cell negative 6 end cell 4 row cell negative 5 end cell 5 3 end table close parentheses end style 

Ke roboguru plus

Iklan

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Iklan

Pembahasan

Diketahui .Kita cari dulu masing-masing nilai minornya lalu kita tentukan kofaktornya. Sehingga kita peroleh matriks kofaktornya adalah Maka, adjoinnya adalah Selanjutnya, kita cari determinan matriks A dengan metode Sarrus. Kita peroleh diagonal kanan = 2 ∙ 1 ∙ 2 + ( - 1) ∙ 0 ∙ 2 + 5 ∙ 1 ∙ ( - 3) = 4 + 0 - 15 = -11 diagonal kiri = 5 ∙ 1 ∙ 2 + 2 ∙ 0 ∙ ( - 3) + ( - 1) ∙ 1 ∙ 2 = 10 + 0 - 2 = 8 Sehingga determinannya adalah determinan = diagonal kanan - diagonal kiri = -11 - 8 = -19 Jadi, invers dari matriks A adalah

Diketahui undefined. Kita cari dulu masing-masing nilai minornya lalu kita tentukan kofaktornya.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell M subscript 11 end cell equals cell open vertical bar table row 1 0 row cell negative 3 end cell 2 end table close vertical bar equals 1 times 2 minus 0 times open parentheses negative 3 close parentheses equals 2 plus 0 equals 2 end cell row cell C subscript 11 end cell equals cell open parentheses negative 1 close parentheses to the power of 1 plus 1 end exponent times M subscript 11 equals open parentheses negative 1 close parentheses squared times 2 equals 1 times 2 equals 2 end cell row cell M subscript 12 end cell equals cell open vertical bar table row 1 0 row 2 2 end table close vertical bar equals 1 times 2 minus 0 times 2 equals 2 minus 0 equals 2 end cell row cell C subscript 12 end cell equals cell open parentheses negative 1 close parentheses to the power of 1 plus 2 end exponent times M subscript 12 equals open parentheses negative 1 close parentheses cubed times 2 equals open parentheses negative 1 close parentheses times 2 equals negative 2 end cell row cell M subscript 13 end cell equals cell open vertical bar table row 1 1 row 2 cell negative 3 end cell end table close vertical bar equals 1 times open parentheses negative 3 close parentheses minus 1 times 2 equals negative 3 minus 2 equals negative 5 end cell row cell C subscript 13 end cell equals cell open parentheses negative 1 close parentheses to the power of 1 plus 3 end exponent times M subscript 13 equals open parentheses negative 1 close parentheses to the power of 4 times open parentheses negative 5 close parentheses equals 1 times open parentheses negative 5 close parentheses equals negative 5 end cell row cell M subscript 21 end cell equals cell open vertical bar table row cell negative 1 end cell 5 row cell negative 3 end cell 2 end table close vertical bar equals open parentheses negative 1 close parentheses times 2 minus 5 times open parentheses negative 3 close parentheses equals negative 2 plus 15 equals 13 end cell row cell C subscript 21 end cell equals cell open parentheses negative 1 close parentheses to the power of 2 plus 1 end exponent times M subscript 21 equals open parentheses negative 1 close parentheses cubed times 13 equals open parentheses negative 1 close parentheses times 13 equals negative 13 end cell row cell M subscript 22 end cell equals cell open vertical bar table row 2 5 row 2 2 end table close vertical bar equals 2 times 2 minus 5 times 2 equals 4 minus 10 equals negative 6 end cell row cell C subscript 22 end cell equals cell open parentheses negative 1 close parentheses to the power of 2 plus 2 end exponent times M subscript 22 equals open parentheses negative 1 close parentheses to the power of 4 times open parentheses negative 6 close parentheses equals 1 times open parentheses negative 6 close parentheses equals negative 6 end cell row cell M subscript 23 end cell equals cell open vertical bar table row 2 cell negative 1 end cell row 2 cell negative 3 end cell end table close vertical bar equals 2 times open parentheses negative 3 close parentheses minus open parentheses negative 1 close parentheses times 2 equals negative 6 plus 2 equals negative 4 end cell row cell C subscript 23 end cell equals cell open parentheses negative 1 close parentheses to the power of 2 plus 3 end exponent times M subscript 23 equals open parentheses negative 1 close parentheses to the power of 5 times open parentheses negative 4 close parentheses equals open parentheses negative 1 close parentheses times open parentheses negative 4 close parentheses equals 4 end cell row cell M subscript 31 end cell equals cell open vertical bar table row cell negative 1 end cell 5 row 1 0 end table close vertical bar equals open parentheses negative 1 close parentheses times 0 minus 5 times 1 equals 0 minus 5 equals negative 5 end cell row cell C subscript 31 end cell equals cell open parentheses negative 1 close parentheses to the power of 3 plus 1 end exponent times M subscript 31 equals open parentheses negative 1 close parentheses to the power of 4 times open parentheses negative 5 close parentheses equals 1 times open parentheses negative 5 close parentheses equals negative 5 end cell row cell M subscript 32 end cell equals cell open vertical bar table row 2 5 row 1 0 end table close vertical bar equals 2 times 0 minus 5 times 1 equals 0 minus 5 equals negative 5 end cell row cell C subscript 32 end cell equals cell open parentheses negative 1 close parentheses to the power of 3 plus 2 end exponent times M subscript 32 equals open parentheses negative 1 close parentheses to the power of 5 times open parentheses negative 5 close parentheses equals open parentheses negative 1 close parentheses times open parentheses negative 5 close parentheses equals 5 end cell row cell M subscript 33 end cell equals cell open vertical bar table row 2 cell negative 1 end cell row 1 1 end table close vertical bar equals 2 times 1 minus open parentheses negative 1 close parentheses times 1 equals 2 plus 1 equals 3 end cell row cell C subscript 33 end cell equals cell open parentheses negative 1 close parentheses to the power of 3 plus 3 end exponent times M subscript 33 equals open parentheses negative 1 close parentheses to the power of 6 times 3 equals 1 times 3 equals 3 end cell row blank blank blank row blank blank blank row blank blank blank end table end style 

Sehingga kita peroleh matriks kofaktornya adalah

begin mathsize 14px style open parentheses table row 2 cell negative 2 end cell cell negative 5 end cell row cell negative 13 end cell cell negative 6 end cell 4 row cell negative 5 end cell 5 3 end table close parentheses end style 

Maka, adjoinnya adalah

begin mathsize 14px style open parentheses table row 2 cell negative 2 end cell cell negative 5 end cell row cell negative 13 end cell cell negative 6 end cell 4 row cell negative 5 end cell 5 3 end table close parentheses to the power of T equals open parentheses table row 2 cell negative 13 end cell cell negative 5 end cell row cell negative 2 end cell cell negative 6 end cell 5 row cell negative 5 end cell 4 3 end table close parentheses end style 

Selanjutnya, kita cari determinan matriks A  dengan metode Sarrus.

Kita peroleh

diagonal kanan = 2 ∙ 1 ∙ 2 + (-1) ∙ 0 ∙ 2 + 5 ∙ 1 ∙ (-3)
                          = 4 + 0 - 15
                          = -11  

diagonal kiri = 5 ∙ 1 ∙ 2 + 2 ∙ 0 ∙ (-3) + (-1) ∙ 1 ∙ 2
                     = 10 + 0 - 2 
                     = 8

Sehingga determinannya adalah

determinan = diagonal kanan - diagonal kiri
                   = -11 - 8
                   = -19 

Jadi, invers dari matriks A adalah

Error converting from MathML to accessible text. 

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

15

Iklan

Iklan

Gold Icon

Klaim Gold gratis sekarang!

Dengan Gold kamu bisa tanya soal ke Forum sepuasnya, lho.

Pertanyaan serupa

Invers dari matriks adalah ....

112

0.0

Jawaban terverifikasi

Diketahui Matriks Z − 1 adalah ....

1

5.0

Jawaban terverifikasi

Iklan

Iklan

Invers dari matriks adalah ....

32

0.0

Jawaban terverifikasi

Invers dari matriks adalah ....

32

0.0

Jawaban terverifikasi

Invers dari matriks adalah ....

112

0.0

Jawaban terverifikasi
Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Download di Google Play

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Bantuan & Panduan

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

[email protected]

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia