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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: a. QP T

Diketahui , tentukan hasil dari matriks berikut:

a.

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H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

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diperoleh .

diperoleh QP to the power of straight T equals open square brackets table row 18 4 row cell negative 2 end cell cell negative 2 end cell end table close square brackets.

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 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

Berdasarkan operasi di atas, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell QP to the power of straight T end cell equals cell open square brackets table row cell negative 2 end cell 4 row 1 5 end table close square brackets open square brackets table row cell negative 7 end cell 1 row cell negative 2 end cell 0 end table close square brackets to the power of T end cell row blank equals cell open square brackets table row cell negative 2 end cell 4 row 1 5 end table close square brackets open square brackets table row cell negative 7 end cell cell negative 2 end cell row 1 0 end table close square brackets end cell row blank equals cell open square brackets table row cell negative 2 open parentheses negative 7 close parentheses plus 4 left parenthesis 1 right parenthesis end cell cell negative 2 left parenthesis negative 2 right parenthesis plus 4 left parenthesis 0 right parenthesis end cell row cell 1 left parenthesis negative 7 right parenthesis plus 5 left parenthesis 1 right parenthesis end cell cell 1 left parenthesis negative 2 right parenthesis plus 5 left parenthesis 0 right parenthesis end cell end table close square brackets end cell row blank equals cell open square brackets table row 18 4 row cell negative 2 end cell cell negative 2 end cell end table close square brackets end cell end table

Jadi, diperoleh QP to the power of straight T equals open square brackets table row 18 4 row cell negative 2 end cell cell negative 2 end cell end table close square brackets.

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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

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