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Determinante von $$$\left[\begin{array}{cc}2 - \lambda & 3\\1 & 2 - \lambda\end{array}\right]$$$
Verwandter Rechner: Kofaktormatrix-Rechner
Ihre Eingabe
Berechne $$$\left|\begin{array}{cc}2 - \lambda & 3\\1 & 2 - \lambda\end{array}\right|$$$.
Lösung
Die Determinante einer 2x2-Matrix ist $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.
$$$\left|\begin{array}{cc}2 - \lambda & 3\\1 & 2 - \lambda\end{array}\right| = \left(2 - \lambda\right)\cdot \left(2 - \lambda\right) - \left(3\right)\cdot \left(1\right) = \lambda^{2} - 4 \lambda + 1$$$
Antwort
$$$\left|\begin{array}{cc}2 - \lambda & 3\\1 & 2 - \lambda\end{array}\right| = \lambda^{2} - 4 \lambda + 1$$$A
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