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Determinant of $$$\left[\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right]$$$

The calculator will find the determinant of the square $$$2$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right]$$$, with steps shown.

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A

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Your Input

Calculate $$$\left|\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right|$$$.

Solution

The determinant of a 2x2 matrix is $$$\left|\begin{array}{cc}a & b\\c & d\end{array}\right| = a d - b c$$$.

$$$\left|\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right| = \left(1 - \lambda\right)\cdot \left(3 - \lambda\right) - \left(2\right)\cdot \left(0\right) = \lambda^{2} - 4 \lambda + 3$$$

Answer

$$$\left|\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right| = \left(\lambda - 3\right) \left(\lambda - 1\right)$$$A