Determinant of [2λ155λ]\left[\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right]

The calculator will find the determinant of the square 22x22 matrix [2λ155λ]\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 2λ155λ\left|\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right|.

Solution

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

2λ155λ=(2λ)(5λ)(1)(5)=λ27λ+5\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

2λ155λ=λ27λ+5\left|\begin{array}{cc}2 - \lambda & 1\\5 & 5 - \lambda\end{array}\right| = \lambda^{2} - 7 \lambda + 5A