Determinanten av $$$\left[\begin{array}{cc}\cosh{\left(t \right)} & 1\\\sinh{\left(t \right)} & 0\end{array}\right]$$$

Kalkylatorn beräknar determinanten för den kvadratiska $$$2$$$x$$$2$$$-matrisen $$$\left[\begin{array}{cc}\cosh{\left(t \right)} & 1\\\sinh{\left(t \right)} & 0\end{array}\right]$$$ med visade steg.

Relaterad kalkylator: Kalkylator för kofaktormatris

Din inmatning

Beräkna $$$\left|\begin{array}{cc}\cosh{\left(t \right)} & 1\\\sinh{\left(t \right)} & 0\end{array}\right|$$$.

Lösning

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

$$$\left|\begin{array}{cc}\cosh{\left(t \right)} & 1\\\sinh{\left(t \right)} & 0\end{array}\right| = \left(\cosh{\left(t \right)}\right)\cdot \left(0\right) - \left(1\right)\cdot \left(\sinh{\left(t \right)}\right) = - \sinh{\left(t \right)}$$$

Svar

$$$\left|\begin{array}{cc}\cosh{\left(t \right)} & 1\\\sinh{\left(t \right)} & 0\end{array}\right| = - \sinh{\left(t \right)}$$$A

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