Roboguru
SD
SMP
SMA
UTBK/SNBT

Iklan

Pertanyaan

Diketahui matriks A = ( − 1 0 ​ − 2 4 ​ ) dan B = ( 2 4 ​ 6 1 ​ ) . Tentukan: b. nilai x − y − z jika dengan D = ( x − 3 2 y − 10 ​ 4 z − 30 272 ​ )

Diketahui matriks dan . Tentukan:

b.  nilai  jika size 14px D size 14px equals size 14px C to the power of size 14px 2 size 14px minus size 14px B dengan

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

02

:

13

:

33

:

16

Klaim

Iklan

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Pembahasan

Matriks . sehingga, dengan , sebagai berikut maka diperoleh, Jadi, .

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A squared end cell equals cell A A end cell row blank equals cell open parentheses table row cell negative 1 end cell cell negative 2 end cell row 0 4 end table close parentheses open parentheses table row cell negative 1 end cell cell negative 2 end cell row 0 4 end table close parentheses end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses plus open parentheses negative 2 close parentheses cross times 0 end cell cell space space space open parentheses negative 1 close parentheses open parentheses negative 2 close parentheses plus left parenthesis negative 2 right parenthesis left parenthesis 4 right parenthesis end cell row cell 0 cross times open parentheses negative 1 close parentheses plus 4 cross times 0 end cell cell 0 cross times open parentheses negative 2 close parentheses plus 4 cross times 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 cell negative 6 end cell row 0 16 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 C equals cell A squared minus B end cell row blank equals cell open parentheses table row 1 cell negative 6 end cell row 0 16 end table close parentheses minus open parentheses table row 2 6 row 4 1 end table close parentheses space end cell row blank equals cell open parentheses table row cell negative 1 end cell cell negative 12 end cell row cell negative 4 end cell 15 end table close parentheses end cell end table end style

Matriks begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row C equals cell open parentheses table row cell negative 1 end cell cell negative 12 end cell row cell negative 4 end cell 15 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 cell C squared end cell equals cell C C end cell row blank equals cell open parentheses table row cell negative 1 end cell cell negative 12 end cell row cell negative 4 end cell 15 end table close parentheses open parentheses table row cell negative 1 end cell cell negative 12 end cell row cell negative 4 end cell 15 end table close parentheses end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses plus open parentheses negative 12 close parentheses open parentheses negative 4 close parentheses space space space end cell cell open parentheses negative 1 close parentheses open parentheses negative 12 close parentheses plus open parentheses negative 12 close parentheses open parentheses 15 close parentheses end cell row cell open parentheses negative 4 close parentheses open parentheses negative 1 close parentheses plus 15 open parentheses negative 4 close parentheses end cell cell open parentheses negative 4 close parentheses open parentheses negative 12 close parentheses plus 15 open parentheses 15 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row 49 cell negative 168 end cell row cell negative 56 end cell 273 end table close parentheses end cell end table end style

sehingga, begin mathsize 14px style D equals C squared minus B end style dengan begin mathsize 14px style D equals open parentheses table row cell x minus 3 end cell cell 4 z minus 30 end cell row cell 2 y minus 10 end cell 272 end table close parentheses end style, sebagai berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row D equals cell C squared minus B end cell row cell open parentheses table row cell x minus 3 end cell cell 4 z minus 30 end cell row cell 2 y minus 10 end cell 272 end table close parentheses end cell equals cell open parentheses table row 49 cell negative 168 end cell row cell negative 56 end cell 273 end table close parentheses minus open parentheses table row 2 6 row 4 1 end table close parentheses end cell row cell open parentheses table row cell x minus 3 end cell cell 4 z minus 30 end cell row cell 2 y minus 10 end cell 272 end table close parentheses end cell equals cell open parentheses table row 47 cell negative 174 end cell row cell negative 60 end cell 272 end table close parentheses end cell end table end style

maka diperoleh,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 3 end cell equals 47 row x equals 50 row cell 4 z minus 30 end cell equals cell negative 174 end cell row cell 4 z end cell equals cell negative 144 end cell row z equals cell negative 36 end cell row cell 2 y minus 10 end cell equals cell negative 60 end cell row cell 2 y end cell equals cell negative 50 end cell row y equals cell negative 25 end cell end table end style

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x minus y minus z end cell equals cell 50 minus left parenthesis negative 25 right parenthesis minus open parentheses negative 36 close parentheses equals 111 end cell end table end style. 

 

 

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

1

Putri Kusumawati

Makasih ❤️ Bantu banget Mudah dimengerti

Iklan

Gold Icon

Klaim Gold gratis sekarang!

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

Pertanyaan serupa

Selesaikan dan tuliskan dalam bentuk paling sederhana. b. ( 1 1 ​ 2 2 ​ ) ( 2 3 ​ 1 2 ​ ) − ( 1 1 ​ 2 2 ​ ) ( 3 2 ​ 1 2 ​ )

1

0.0

Jawaban terverifikasi

Nilai 2x - y dari persamaan matriks adalah ....

53

5.0

Jawaban terverifikasi

Iklan

If A = ( 2 0 ​ 1 3 ​ ) and B = ( 2 0 ​ 2 3 ​ ) , find the matrices A 2 , B 2 , ( A + B ) ( A − B ) and A 2 − B 2 . Is A 2 − B 2 = ( A + B ) ( A − B ) ?

4

3.0

Jawaban terverifikasi

Diketahui Matriks K = [ 1 2 ​ − 5 3 ​ ] , L = [ 3 − 1 ​ − 2 4 ​ ] dan M = [ 3 5 ​ − 4 − 2 ​ ] . Jika berlaku P = K − L M . Transpos Matriks P adalah ....

3

0.0

Jawaban terverifikasi

Jika matriks-matriks A dan B berordo 2 × 2 mempunyai sifat A ⋅ B  = B ⋅ A , tunjukkanlah: b. ( 2 A − 3 B ) ( A + 2 B ) = 2 A 2 + 4 A B − 3 B A − 6 B 2

1

5.0

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