Roboguru
SD
SMP
SMA
UTBK/SNBT

Iklan

Iklan

Pertanyaan

Diketahui Matriks Z − 1 adalah ....

Diketahui begin mathsize 14px style Z equals open parentheses table row 14 6 cell negative 7 end cell row 6 2 3 row 1 2 10 end table close parentheses end style  Matriks  adalah ....

  1. begin mathsize 14px style negative 1 over 146 open parentheses table row cell negative 14 end cell 74 cell negative 32 end cell row 57 cell negative 147 end cell 22 row cell negative 10 end cell 84 8 end table close parentheses end style 

  2. table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell size 14px 1 over size 14px 216 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 14 cell negative 74 end cell 32 row cell negative 57 end cell 147 cell negative 84 end cell row 10 cell negative 22 end cell cell negative 8 end cell end table close parentheses end cell end table    

  3. begin mathsize 14px style negative 1 over 146 open parentheses table row 14 cell negative 57 end cell 10 row cell negative 74 end cell 147 cell negative 22 end cell row 32 cell negative 84 end cell cell negative 8 end cell end table close parentheses end style 

  4. negative size 14px 1 over size 14px 216 begin mathsize 14px style open parentheses table row 14 cell negative 74 end cell 32 row cell negative 57 end cell 147 cell negative 84 end cell row 10 cell negative 22 end cell cell negative 8 end cell end table close parentheses end style size 14px space    

  5. begin mathsize 14px style negative 1 over 146 open parentheses table row 14 cell negative 74 end cell 32 row cell negative 57 end cell 147 cell negative 84 end cell row 10 cell negative 22 end cell cell negative 8 end cell end table close parentheses end style 

Ke roboguru plus

Iklan

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Iklan

Pembahasan

Sehingga kita peroleh matriks kofaktornya adalah Jadi, adjoinnya adalah Selanjutnya, kita cari determinan matriks C dengan metode Sarrus. Kita peroleh diagonal kanan = 14 ∙ 2 ∙ 10 + 6 ∙ 3 ∙ 1 + ( - 7) ∙ 6 ∙ 2 = 280 + 18 - 84 = 214 diagonal kiri = ( - 7) ∙ 2 ∙ 1 + 14 ∙ 3 ∙ 2 + 6 ∙ 6 ∙ 10 = -14+ 84 + 360 = 430 Sehingga determinannya adalah determinan = diagonal kanan - diagonal kiri = 214- 430 = -216 Jadi, invers dari matriks Z adalah

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 2 3 row 2 10 end table close vertical bar equals 2 times 10 minus 3 times 2 equals 20 minus 6 equals 14 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 14 equals 1 times 14 equals 14 end cell row cell M subscript 12 end cell equals cell open vertical bar table row 6 3 row 1 10 end table close vertical bar equals 6 times 10 minus 3 times 1 equals 60 minus 3 equals 57 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 57 equals open parentheses negative 1 close parentheses times 57 equals negative 57 end cell row cell M subscript 13 end cell equals cell open vertical bar table row 6 2 row 1 2 end table close vertical bar equals 6 times 2 minus 2 times 1 equals 12 minus 2 equals 10 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 10 equals 1 times 10 equals 10 end cell row cell M subscript 21 end cell equals cell open vertical bar table row 6 cell negative 7 end cell row 2 10 end table close vertical bar equals 6 times 10 minus open parentheses negative 7 close parentheses times 2 equals 60 plus 14 equals 74 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 74 equals open parentheses negative 1 close parentheses times 74 equals negative 74 end cell row cell M subscript 22 end cell equals cell open vertical bar table row 14 cell negative 7 end cell row 1 10 end table close vertical bar equals 14 times 10 minus open parentheses negative 7 close parentheses times 1 equals 140 plus 7 equals 147 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 147 equals 1 times 147 equals 147 end cell row cell M subscript 23 end cell equals cell open vertical bar table row 14 6 row 1 2 end table close vertical bar equals 14 times 2 minus 6 times 1 equals 28 minus 6 equals 22 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 22 equals open parentheses negative 1 close parentheses times 22 equals negative 22 end cell row cell M subscript 31 end cell equals cell open vertical bar table row 6 cell negative 7 end cell row 2 3 end table close vertical bar equals 6 times 3 minus open parentheses negative 7 close parentheses times 2 equals 18 plus 14 equals 32 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 32 equals 1 times 32 equals 32 end cell row cell M subscript 32 end cell equals cell open vertical bar table row 14 cell negative 7 end cell row 6 3 end table close vertical bar equals 14 times 3 minus open parentheses negative 7 close parentheses times 6 equals 42 plus 42 equals 84 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 84 equals open parentheses negative 1 close parentheses times 84 equals negative 84 end cell row cell M subscript 33 end cell equals cell open vertical bar table row 14 6 row 6 2 end table close vertical bar equals 14 times 2 minus 6 times 6 equals 28 minus 36 equals negative 8 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 open parentheses negative 8 close parentheses equals 1 times open parentheses negative 8 close parentheses equals negative 8 end cell end table end style 

Sehingga kita peroleh matriks kofaktornya adalah

begin mathsize 14px style open parentheses table row 14 cell negative 57 end cell 10 row cell negative 74 end cell 147 cell negative 22 end cell row 32 cell negative 84 end cell cell negative 8 end cell end table close parentheses end style 

Jadi, adjoinnya adalah

begin mathsize 14px style open parentheses table row 14 cell negative 57 end cell 10 row cell negative 74 end cell 147 cell negative 22 end cell row 32 cell negative 84 end cell cell negative 8 end cell end table close parentheses to the power of T equals open parentheses table row 14 cell negative 74 end cell 32 row cell negative 57 end cell 147 cell negative 84 end cell row 10 cell negative 22 end cell cell negative 8 end cell end table close parentheses end style 

Selanjutnya, kita cari determinan matriks C dengan metode Sarrus.

Kita peroleh

diagonal kanan = 14 ∙ 2 ∙ 10 + 6 ∙ 3 ∙ 1 + (-7) ∙ 6 ∙ 2
                         = 280 + 18 - 84 
                         = 214

diagonal kiri = (-7) ∙ 2 ∙ 1 + 14 ∙ 3 ∙ 2 + 6 ∙ 6 ∙ 10
                    = -14 + 84 + 360
                    = 430

Sehingga determinannya adalah

determinan = diagonal kanan - diagonal kiri
                   = 214 - 430
                   = -216

Jadi, invers dari matriks Z adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px D to the power of size 14px minus size 14px 1 end exponent end cell size 14px equals cell fraction numerator size 14px 1 over denominator begin mathsize 14px style vertical line Z vertical line end style end fraction size 14px a size 14px d size 14px j size 14px size 14px Z end cell row blank size 14px equals cell size 14px minus size 14px 1 over size 14px 216 begin mathsize 14px style open parentheses table row 14 cell negative 74 end cell 32 row cell negative 57 end cell 147 cell negative 84 end cell row 10 cell negative 22 end cell cell negative 8 end cell end table close parentheses end style end cell end table    

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

1

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

Invers dari matriks adalah ....

15

0.0

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 ....

15

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