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Diketahui P = [ − 7 − 2 ​ 1 0 ​ ] , Q = [ − 2 1 ​ 4 5 ​ ] dan R = [ − 4 0 ​ 1 − 2 ​ ] , tentukan hasil dari matriks berikut: b. 2 R 2 − 4 Q T

Diketahui , tentukan hasil dari matriks berikut:

b.

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diperoleh .

diperoleh 2 straight R squared minus 4 straight Q to the power of straight T equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row 40 cell negative 28 end cell row cell negative 4 end cell cell negative 12 end cell end table close square brackets end cell end table.

Pembahasan

Ingat operasi perkalian matriks dan transpos matriks berikut: Berdasarkan operasi di atas, maka Jadi, diperoleh .

Ingat operasi perkalian matriks dan transpos matriks berikut:

rightwards double arrow straight k open square brackets table row straight a straight b row straight c straight d end table close square brackets equals open square brackets table row ka kb row kc kd end table close square brackets rightwards double arrow open square brackets table row straight a straight b row straight c straight d end table close square brackets open square brackets table row straight e straight f row straight g straight h end table close square brackets equals open square brackets table row cell ae plus bg end cell cell af plus bh end cell row cell ce plus dg end cell cell cf plus dh end cell end table close square brackets rightwards double arrow open square brackets table row straight a straight b row straight c straight d end table close square brackets to the power of straight T equals open square brackets table row straight a straight c row straight b straight d end table close square brackets rightwards double arrow open square brackets table row straight a straight b row straight c straight d end table close square brackets minus open square brackets table row straight e straight f row straight g straight h end table close square brackets equals open square brackets table row cell straight a minus straight e end cell cell straight b minus straight f end cell row cell straight c minus straight g end cell cell straight d minus straight h end cell end table close square brackets

Berdasarkan operasi di atas, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight R squared minus 4 straight Q to the power of straight T end cell equals cell 2 open square brackets table row cell negative 4 end cell 1 row 0 cell negative 2 end cell end table close square brackets open square brackets table row cell negative 4 end cell 1 row 0 cell negative 2 end cell end table close square brackets minus 4 open square brackets table row cell negative 2 end cell 4 row 1 5 end table close square brackets to the power of straight T end cell row blank equals cell 2 open square brackets table row cell 16 plus 0 end cell cell negative 4 minus 2 end cell row cell 0 plus 0 end cell cell 0 plus 4 end cell end table close square brackets minus 4 open square brackets table row cell negative 2 end cell 4 row 1 5 end table close square brackets end cell row blank equals cell open square brackets table row 32 cell negative 12 end cell row 0 8 end table close square brackets minus open square brackets table row cell negative 8 end cell 16 row 4 20 end table close square brackets end cell row blank equals cell open square brackets table row 40 cell negative 28 end cell row cell negative 4 end cell cell negative 12 end cell end table close square brackets end cell end table

Jadi, diperoleh 2 straight R squared minus 4 straight Q to the power of straight T equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets table row 40 cell negative 28 end cell row cell negative 4 end cell cell negative 12 end cell end table close square brackets end cell end table.

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Diketahui matriks A = ⎣ ⎡ ​ − 1 0 − 3 ​ 0 2 1 ​ 3 1 0 ​ ⎦ ⎤ ​ dan B = ⎣ ⎡ ​ − 5 − 3 − 7 ​ − 1 0 − 3 ​ 3 − 3 − 2 ​ ⎦ ⎤ ​ . Tentukan nilai dari A − B T !

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