Determinant of $$$\left[\begin{array}{cc}1 - \lambda & 3\\1 & - \lambda - 1\end{array}\right]$$$
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Your Input
Calculate $$$\left|\begin{array}{cc}1 - \lambda & 3\\1 & - \lambda - 1\end{array}\right|$$$.
Solution
The determinant of a 2x2 matrix is $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.
$$$\left|\begin{array}{cc}1 - \lambda & 3\\1 & - \lambda - 1\end{array}\right| = \left(1 - \lambda\right)\cdot \left(- \lambda - 1\right) - \left(3\right)\cdot \left(1\right) = \lambda^{2} - 4$$$
Answer
$$$\left|\begin{array}{cc}1 - \lambda & 3\\1 & - \lambda - 1\end{array}\right| = \lambda^{2} - 4$$$A