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Diketahui A=(1−3​21​), B=(0x​−13​), dan C=(y7​−27​) . Jika det(AB)=det(−C), maka nilai x−y adalah ....

Pertanyaan

Diketahui begin mathsize 14px style straight A equals open parentheses table row 1 2 row cell negative 3 end cell 1 end table close parentheses comma space straight B equals open parentheses table row 0 cell negative 1 end cell row straight x 3 end table close parentheses comma space dan space straight C equals open parentheses table row straight y cell negative 2 end cell row 7 7 end table close parentheses end style . Jika begin mathsize 14px style d e t left parenthesis A B right parenthesis equals d e t left parenthesis negative C right parenthesis end style, maka nilai begin mathsize 14px style x minus y end style adalah ....

  1. begin mathsize 14px style 2 end style 

  2. begin mathsize 14px style 1 half end style 

  3. begin mathsize 14px style negative 1 fourth end style 

  4. begin mathsize 14px style negative 1 half end style 

  5. begin mathsize 14px style negative 2 end style 

A. Acfreelance

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Dengan menggunakan sifat

begin mathsize 14px style det left parenthesis AB right parenthesis equals det space straight A times det space straight B det left parenthesis kC subscript nxn right parenthesis equals straight k to the power of straight n times det space straight C end style 

 

dan diketahui matriks C berordo 2 × 2, maka kita peroleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell det left parenthesis AB right parenthesis end cell equals cell det left parenthesis negative straight C right parenthesis end cell row cell det space straight A times det space straight B end cell equals cell left parenthesis negative 1 right parenthesis squared times det space straight C end cell row cell left parenthesis 1 times 1 minus 2 times left parenthesis negative 3 right parenthesis right parenthesis left parenthesis 0 times 3 minus left parenthesis negative 1 right parenthesis times straight x right parenthesis end cell equals cell 1 times left parenthesis straight y times 7 minus left parenthesis negative 2 right parenthesis times 7 right parenthesis end cell row cell left parenthesis 1 plus 6 right parenthesis left parenthesis 0 plus straight x right parenthesis end cell equals cell 1 left parenthesis 7 straight y plus 14 right parenthesis end cell row cell left parenthesis 7 right parenthesis left parenthesis straight x right parenthesis end cell equals cell 7 straight y plus 14 end cell row cell space 7 straight x end cell equals cell 7 straight y plus 14 space end cell row cell 7 straight x minus 7 straight y end cell equals 14 row cell 7 left parenthesis straight x minus straight y right parenthesis end cell equals 14 row cell space straight x minus straight y end cell equals cell 14 over 7 end cell row cell space straight x minus straight y end cell equals cell 2 space end cell row blank blank blank row blank blank blank row blank blank blank end table end style 

Jadi, nilai undefined adalah 2.

Dengan demikian, jawaban yang tepat adalah A.

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