Jika vektor \( \vec{a} = 2\hat{i} + 3 \hat{j}, \ \vec{b} = 3\hat{i}+\hat{j} \) dan \( \vec{p} = -5 \hat{i} -4\hat{j} \). Jika \( \vec{p} = k \vec{a} -m \vec{b} \), maka nilai \(k-m\) adalah…
- 5
- 3
- -2
- 6
- -9
Pembahasan:
Untuk \( \vec{p} = k \vec{a} -m \vec{b} \), kita peroleh berikut:
\begin{aligned} \vec{p} &= k \vec{a}-m \vec{b} \\[8pt] \begin{pmatrix} -5 \\[8pt] -4 \end{pmatrix} &= k \begin{pmatrix} 2 \\[8pt] 3 \end{pmatrix} - m \begin{pmatrix} 3 \\[8pt] 1 \end{pmatrix} \\[8pt] \begin{pmatrix} -5 \\[8pt] -4 \end{pmatrix} &= \begin{pmatrix} 2k-3m \\[8pt] 3k-m \end{pmatrix} \\[8pt] 2k-3m &= -5 \\[8pt] 3k-m &= -4 \\[8pt] \text{Solusi SPLDV} &: \ k = -1 \ \text{dan} \ m = 1 \\[8pt] k-m &= -1-1=-2 \end{aligned}
Jawaban C.