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Determinant of $$$\left[\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right]$$$

The calculator will find the determinant of the square $$$2$$$x$$$2$$$ matrix $$$\left[\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right]$$$, with steps shown.

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A

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Your Input

Calculate $$$\left|\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right|$$$.

Solution

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

$$$\left|\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right| = \left(2 - \lambda\right)\cdot \left(5 - \lambda\right) - \left(1\right)\cdot \left(5\right) = \lambda^{2} - 7 \lambda + 5$$$

Answer

$$$\left|\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right| = \lambda^{2} - 7 \lambda + 5$$$A