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

Pertanyaan

Diketahui vektor-vektor $\overrightarrow a=\begin{pmatrix}4\\-2\end{pmatrix}$ dan $\overrightarrow b=\begin{pmatrix}-2\\3\end{pmatrix}$ . Kombinasi linear dari $3\overrightarrow a+2\overrightarrow b$ adalah ....

$negative 8 i with rightwards arrow on top$
$8 i with rightwards arrow on top$
$8 j with rightwards arrow on top$
$negative 8 i with rightwards arrow on top minus 12 j with rightwards arrow on top$
$8 i with rightwards arrow on top plus 12 j with rightwards arrow on top$

Pembahasan Soal:

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.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

P. Afrisno

Mahasiswa/Alumni Universitas Sebelas Maret

Terakhir diupdate 06 Oktober 2021