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Determinanten av $$$\left[\begin{array}{cc}1 - \lambda & \frac{1}{5}\\\frac{1}{5} & 1 - \lambda\end{array}\right]$$$
Relaterad kalkylator: Kalkylator för kofaktormatris
Din inmatning
Beräkna $$$\left|\begin{array}{cc}1 - \lambda & \frac{1}{5}\\\frac{1}{5} & 1 - \lambda\end{array}\right|$$$.
Lösning
Determinanten för en 2x2-matris är $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.
$$$\left|\begin{array}{cc}1 - \lambda & \frac{1}{5}\\\frac{1}{5} & 1 - \lambda\end{array}\right| = \left(1 - \lambda\right)\cdot \left(1 - \lambda\right) - \left(\frac{1}{5}\right)\cdot \left(\frac{1}{5}\right) = \lambda^{2} - 2 \lambda + \frac{24}{25}$$$
Svar
$$$\left|\begin{array}{cc}1 - \lambda & \frac{1}{5}\\\frac{1}{5} & 1 - \lambda\end{array}\right| = \lambda^{2} - 2 \lambda + \frac{24}{25} = \lambda^{2} - 2 \lambda + 0.96$$$A