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Diketahui vektor-vektor a=(4−2​) dan b=(−23​). Kombinasi linear dari 3a+2b adalah ....

Pertanyaan

Diketahui vektor-vektor a with rightwards arrow on top equals open parentheses table row 4 row cell negative 2 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 3 end table close parentheses. Kombinasi linear dari 3 a with rightwards arrow on top plus 2 b with rightwards arrow on top adalah ....

  1. negative 8 i with rightwards arrow on top 

  2. 8 i with rightwards arrow on top 

  3. 8 j with rightwards arrow on top 

  4. negative 8 i with rightwards arrow on top minus 12 j with rightwards arrow on top 

  5. 8 i with rightwards arrow on top plus 12 j with rightwards arrow on top 

P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Jika diberikan vektor-vektor a with rightwards arrow on top equals open parentheses table row cell x subscript 1 end cell row cell y subscript 1 end cell end table close parentheses space dan space b with rightwards arrow on top equals open parentheses table row cell x subscript 2 end cell row cell y subscript 2 end cell end table close parentheses dan skalar m space dan space n maka kombinasi linear dari m a with rightwards arrow on top plus n b with rightwards arrow on top dapat ditentukan dengan rumus berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell m a with rightwards arrow on top plus n b with rightwards arrow on top end cell equals cell m open parentheses table row cell x subscript 1 end cell row cell y subscript 1 end cell end table close parentheses plus n open parentheses table row cell x subscript 2 end cell row cell y subscript 2 end cell end table close parentheses end cell row blank equals cell open parentheses m x subscript 1 plus n x subscript 2 close parentheses i with rightwards arrow on top plus open parentheses m y subscript 1 plus n y subscript 2 close parentheses j with rightwards arrow on top end cell end table 

Sehingga untuk vektor a with rightwards arrow on top equals open parentheses table row 4 row cell negative 2 end cell end table close parentheses space dan space b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 3 end table close parentheses dapat ditentukan kombinasi linear 3 a with rightwards arrow on top plus 2 b with rightwards arrow on top sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a with rightwards arrow on top plus 2 b with rightwards arrow on top end cell equals cell 3 open parentheses table row 4 row cell negative 2 end cell end table close parentheses plus 2 open parentheses table row cell negative 2 end cell row 3 end table close parentheses end cell row blank equals cell open parentheses table row 12 row cell negative 6 end cell end table close parentheses plus open parentheses table row cell negative 4 end cell row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell 12 minus 4 end cell row cell negative 6 plus 6 end cell end table close parentheses end cell row blank equals cell open parentheses table row 8 row 0 end table close parentheses end cell row blank equals cell 8 i with rightwards arrow on top plus 0 k with rightwards arrow on top end cell row blank equals cell 8 i with rightwards arrow on top end cell end table 

Jadi, jawaban yang benar adalah B.

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