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

Nilai 2x - y dari persamaan matriks begin mathsize 14px style open parentheses table row 5 cell 3 x end cell row cell y minus 1 end cell 2 end table close parentheses minus open parentheses table row 7 cell 1 minus 2 y end cell row cell 2 x end cell 6 end table close parentheses equals open parentheses table row 6 2 row cell negative 4 end cell 8 end table close parentheses open parentheses table row 0 3 row cell negative 1 end cell 1 end table close parentheses end style adalah ....

  1. -7

  2. -1

  3. 1

  4. 7

  5. 8

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Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

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Pembahasan

begin mathsize 14px style bold i bold right parenthesis bold space Operasikan space matriks  open parentheses table row 5 cell 3 straight x end cell row cell straight y minus 1 end cell 2 end table close parentheses minus open parentheses table row 7 cell 1 minus 2 straight y end cell row cell 2 straight x end cell 6 end table close parentheses equals open parentheses table row 6 2 row cell negative 4 end cell 8 end table close parentheses open parentheses table row 0 3 row cell negative 1 end cell 1 end table close parentheses  open parentheses table row cell 5 minus 7 end cell cell 3 straight x minus open parentheses 1 minus 2 straight y close parentheses end cell row cell open parentheses straight y minus 1 close parentheses minus 2 straight x end cell cell 2 minus 6 end cell end table close parentheses equals open parentheses table row cell 6.0 plus 2. open parentheses negative 1 close parentheses end cell cell 6.3 plus 2.1 end cell row cell open parentheses negative 4 close parentheses.0 plus 8. open parentheses negative 1 close parentheses end cell cell open parentheses negative 4 close parentheses.3 plus 8.1 end cell end table close parentheses  open parentheses table row cell negative 2 end cell cell 3 straight x plus 2 straight y minus 1 end cell row cell straight y minus 2 straight x minus 1 end cell cell negative 4 end cell end table close parentheses equals open parentheses table row cell negative 2 end cell 20 row cell negative 8 end cell cell negative 4 end cell end table close parentheses    bold ii bold right parenthesis bold space Perhatikan space elemen minus elemen space matriks space yang space seletak  Dari space baris space 1 space kolom space 2 space didapat  3 straight x plus 2 straight y minus 1 equals 20  3 straight x plus 2 straight y equals 21    Dari space baris space 2 space kolom space 1 space didapat  straight y minus 2 straight x minus 1 equals negative 8  straight y minus 2 straight x equals negative 7    Sehingga space didapat space sistem space persamaan  open curly brackets table row cell 3 straight x plus 2 straight y equals 21 end cell cell horizontal ellipsis open parentheses 1 close parentheses end cell row cell straight y minus 2 straight x equals negative 7 end cell cell horizontal ellipsis open parentheses 2 close parentheses end cell end table close    bold iii bold right parenthesis space Eliminasi space sistem space persamaan  left parenthesis 1 right parenthesis space space space 3 straight x plus 2 straight y equals 21 vertical line cross times 1 vertical line 3 straight x plus 2 straight y equals 21  left parenthesis 2 right parenthesis space space space space straight y minus 2 straight x equals negative 7 vertical line cross times 2 vertical line bottom enclose 2 straight y minus 4 straight x equals negative 14 space space space minus end enclose  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 7 straight x equals 35 rightwards arrow straight x equals 5    bold iv bold right parenthesis space Substitusi space straight x space ke space persamaan space left parenthesis 2 right parenthesis  left parenthesis 2 right parenthesis space space straight y minus 2 straight x equals negative 7  space space space space space space straight y minus 2 left parenthesis 5 right parenthesis equals negative 7  space space space space space space straight y minus 10 equals negative 7  space space space space space space straight y equals negative 7 plus 10  space space space space space space straight y equals 3    bold v bold right parenthesis space Hitung space 2 straight x minus straight y  2 straight x minus straight y equals 2 open parentheses 5 close parentheses minus 3 equals 10 minus 3 equals 7 end style

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Diketahui matriks A = ( − 2 x − 2 ​ 5 y ​ ) , B = ( y − 2 ​ 2 3 ​ ) , dan C = ( 5 4 ​ − 1 12 ​ ) .Jika 3 B t = C − A dan adalah transpos dari matriks B, hitunglah nilai x 2 − y 2 .

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