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Diketahui persamaan matriks Nilai dari adalah ....

Diketahui persamaan matriks

begin mathsize 14px style 2 open parentheses table row a 2 row cell negative 3 end cell 1 end table close parentheses plus open parentheses table row 4 cell negative 1 end cell row 0 b end table close parentheses equals open parentheses table row 3 2 row c 4 end table close parentheses open parentheses table row 2 d row 1 3 end table close parentheses end style 

Nilai dari begin mathsize 14px style a plus b plus c plus d end style adalah ....

  1. begin mathsize 14px style horizontal ellipsis end style 

  2. begin mathsize 14px style horizontal ellipsis end style 

Jawaban:

Penjumlahan matriks pada ruas kiri persamaan matriks di atas dapat dihitung seperti berikut,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 open parentheses table row a 2 row cell negative 3 end cell 1 end table close parentheses plus open parentheses table row 4 cell negative 1 end cell row 0 b end table close parentheses end cell row blank equals cell open parentheses table row cell 2 times a end cell cell 2 times 2 end cell row cell 2 times left parenthesis negative 3 right parenthesis end cell cell 2 times 1 end cell end table close parentheses plus open parentheses table row 4 cell negative 1 end cell row 0 b end table close parentheses end cell row blank equals cell open parentheses table row cell 2 a end cell 4 row cell negative 6 end cell 2 end table close parentheses plus open parentheses table row 4 cell negative 1 end cell row 0 b end table close parentheses end cell row blank equals cell open parentheses table row cell 2 a plus 4 end cell cell 4 minus 1 end cell row cell negative 6 plus 0 end cell cell 2 plus b end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 a plus 4 end cell 3 row cell negative 6 end cell cell 2 plus b end cell end table close parentheses end cell end table end style  

Penyelesaian perkalian matriks pada ruas kanan yaitu,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row 3 2 row c 4 end table close parentheses open parentheses table row 2 d row 1 3 end table close parentheses end cell equals cell open parentheses table row cell 3 times 2 plus 2 times 1 end cell cell 3 times d plus 2 times 3 end cell row cell c times 2 plus 4 times 1 end cell cell c times d plus 4 times 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 6 plus 2 end cell cell 3 d plus 6 end cell row cell 2 c plus 4 end cell cell c d plus 12 end cell end table close parentheses end cell row blank equals cell open parentheses table row 8 cell 3 d plus 6 end cell row cell 2 c plus 4 end cell cell c d plus 12 end cell end table close parentheses end cell end table end style 

Diketahui hasil dari penjumlahan matriks di ruas kiri sama dengan perkalian matriks di ruas kanan, maka

begin mathsize 14px style open parentheses table row cell 2 a plus 4 end cell 3 row cell negative 6 end cell cell 2 plus b end cell end table close parentheses equals open parentheses table row 8 cell 3 d plus 6 end cell row cell 2 c plus 4 end cell cell c d plus 12 end cell end table close parentheses end style.

Apabila terdapat dua matriks yang sama, maka anggota-anggota dengan letak yang sama nilainya akan sama pula, sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a plus 4 end cell equals 8 row cell 2 a end cell equals cell 8 minus 4 end cell row cell 2 a end cell equals 4 row a equals 2 end table end style     begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 d plus 6 end cell equals 3 row cell 3 d end cell equals cell 3 minus 6 end cell row cell 3 d end cell equals cell negative 3 end cell row d equals cell negative 1 end cell end table end style      begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 c plus 4 end cell equals cell negative 6 end cell row cell 2 c end cell equals cell negative 6 minus 4 end cell row cell 2 c end cell equals cell negative 10 end cell row c equals cell negative 5 end cell end table end style 

Didapatkan nilai begin mathsize 14px style a equals 2 comma space c equals negative 5 comma space dan space d equals negative 1 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 plus b end cell equals cell c d plus 12 end cell row cell 2 plus b end cell equals cell left parenthesis negative 5 right parenthesis times left parenthesis negative 1 right parenthesis plus 12 end cell row cell 2 plus b end cell equals cell 5 plus 12 end cell row cell 2 plus b end cell equals 17 row b equals cell 17 minus 2 end cell row b equals 15 end table end style 

Penjumlahan dari keempat variabel tersebut adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a plus b plus c plus d end cell row blank equals cell 2 plus 15 plus left parenthesis negative 5 right parenthesis plus left parenthesis negative 1 right parenthesis end cell row blank equals 23 end table end style 

Jadi, nilai dari begin mathsize 14px style a plus b plus c plus d end style adalah begin mathsize 14px style 23 end style.

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