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Determinan dari $$$\left[\begin{array}{cc}\cos{\left(\theta \right)} & - r \sin{\left(\theta \right)}\\\sin{\left(\theta \right)} & r \cos{\left(\theta \right)}\end{array}\right]$$$
Kalkulator terkait: Kalkulator Matriks Kofaktor
Masukan Anda
Hitung $$$\left|\begin{array}{cc}\cos{\left(\theta \right)} & - r \sin{\left(\theta \right)}\\\sin{\left(\theta \right)} & r \cos{\left(\theta \right)}\end{array}\right|$$$.
Solusi
Determinan matriks 2x2 adalah $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.
$$$\left|\begin{array}{cc}\cos{\left(\theta \right)} & - r \sin{\left(\theta \right)}\\\sin{\left(\theta \right)} & r \cos{\left(\theta \right)}\end{array}\right| = \left(\cos{\left(\theta \right)}\right)\cdot \left(r \cos{\left(\theta \right)}\right) - \left(- r \sin{\left(\theta \right)}\right)\cdot \left(\sin{\left(\theta \right)}\right) = r$$$
Jawaban
$$$\left|\begin{array}{cc}\cos{\left(\theta \right)} & - r \sin{\left(\theta \right)}\\\sin{\left(\theta \right)} & r \cos{\left(\theta \right)}\end{array}\right| = r$$$A