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  1. Beranda
  2. Kalkulator
  3. Kalkulator: Aljabar Linear
  4. Kalkulator Aljabar Linear

Determinan dari $$$\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right]$$$

Kalkulator akan menghitung determinan dari matriks persegi $$$2$$$x$$$2$$$ $$$\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right]$$$, dengan langkah-langkah yang ditampilkan.

Kalkulator terkait: Kalkulator Matriks Kofaktor

A

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Masukan Anda

Hitung $$$\left|\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right|$$$.

Solusi

Determinan matriks 2x2 adalah $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

$$$\left|\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right| = \left(\frac{\sqrt{3}}{2}\right)\cdot \left(- \sin{\left(t \right)}\right) - \left(\frac{\cos{\left(t \right)}}{2}\right)\cdot \left(0\right) = - \frac{\sqrt{3} \sin{\left(t \right)}}{2}$$$

Jawaban

$$$\left|\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right| = - \frac{\sqrt{3} \sin{\left(t \right)}}{2}\approx - 0.866025403784439 \sin{\left(t \right)}$$$A


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