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

Kalkylatorn beräknar determinanten för den kvadratiska $$$2$$$x$$$2$$$-matrisen $$$\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{\cos{\left(t \right)}}{2}\\0 & - \sin{\left(t \right)}\end{array}\right]$$$ med visade steg.

Relaterad kalkylator: Kalkylator för kofaktormatris

Din inmatning

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

Lösning

Determinanten för en 2x2-matris är $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

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

Svar

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

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