Diketahui matriks-matriks: A=(21​12​); B=(11​10​); C=(11​−11​). Tentukan invers matriks (A+2B−3C).

Pertanyaan

Diketahui matriks-matriks: A equals open parentheses table row 2 1 row 1 2 end table close parenthesesB equals open parentheses table row 1 1 row 1 0 end table close parenthesesC equals open parentheses table row 1 cell negative 1 end cell row 1 1 end table close parentheses. Tentukan invers matriks open parentheses A plus 2 B minus 3 C close parentheses.

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

invers matriks open parentheses A plus 2 B minus 3 C close parentheses adalah open parentheses table row 1 6 row 0 cell negative 1 end cell end table close parentheses.

Pembahasan

Rumus perkalian skalar k dengan matriks 2 cross times 2 yaitu:

k times open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k times a end cell cell k times b end cell row cell k times c end cell cell k times d end cell end table close parentheses

Tentukan terlebih dahulu matriks dari open parentheses A plus 2 B minus 3 C close parentheses.

Dengan operasi hitung matriks, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell A plus 2 B minus 3 C end cell equals cell open parentheses table row 2 1 row 1 2 end table close parentheses plus 2 open parentheses table row 1 1 row 1 0 end table close parentheses minus 3 open parentheses table row 1 cell negative 1 end cell row 1 1 end table close parentheses end cell row blank equals cell open parentheses table row 2 1 row 1 2 end table close parentheses plus open parentheses table row cell 2 times 1 end cell cell 2 times 1 end cell row cell 2 times 1 end cell cell 2 times 0 end cell end table close parentheses minus open parentheses table row cell 3 times 1 end cell cell 3 times open parentheses negative 1 close parentheses end cell row cell 3 times 1 end cell cell 3 times 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 1 row 1 2 end table close parentheses plus open parentheses table row 2 2 row 2 0 end table close parentheses minus open parentheses table row 3 cell negative 3 end cell row 3 3 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 plus 2 minus 3 end cell cell 1 plus 2 minus open parentheses negative 3 close parentheses end cell row cell 1 plus 2 minus 3 end cell cell 2 plus 0 minus 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 cell 3 plus 3 end cell row 0 cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 6 row 0 cell negative 1 end cell end table close parentheses end cell end table

Kemudian tentukan inversnya.

Rumus invers matriks 2 cross times 2 yaitu:

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 open parentheses table row a b row c d end table close parentheses to the power of negative 1 end exponent end cell row blank 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 times d minus b times 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

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses A plus 2 B minus 3 C close parentheses end cell equals cell open parentheses table row 1 6 row 0 cell negative 1 end cell end table close parentheses end cell row cell open parentheses A plus 2 B minus 3 C close parentheses to the power of negative 1 end exponent end cell equals cell open parentheses table row 1 6 row 0 cell negative 1 end cell end table close parentheses to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 1 over denominator 1 open parentheses negative 1 close parentheses minus 6 open parentheses 0 close parentheses end fraction open parentheses table row cell negative 1 end cell cell negative 6 end cell row 0 1 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator negative 1 minus 0 end fraction open parentheses table row cell negative 1 end cell cell negative 6 end cell row 0 1 end table close parentheses end cell row blank equals cell negative 1 over 1 open parentheses table row cell negative 1 end cell cell negative 6 end cell row 0 1 end table close parentheses end cell row blank equals cell negative 1 times open parentheses table row cell negative 1 end cell cell negative 6 end cell row 0 1 end table close parentheses end cell row blank equals cell open parentheses table row 1 6 row 0 cell negative 1 end cell end table close parentheses end cell end table

Dengan demikian, invers matriks open parentheses A plus 2 B minus 3 C close parentheses adalah open parentheses table row 1 6 row 0 cell negative 1 end cell end table close parentheses.

70

0.0 (0 rating)

Pertanyaan serupa

Diketahui matriks  dan matriks . Jika 2AB−I=C, matriks B adalah ...

75

3.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

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