Determinant of [1λ203λ]\left[\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right]

The calculator will find the determinant of the square 22x22 matrix [1λ203λ]\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 1λ203λ\left|\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \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.

1λ203λ=(1λ)(3λ)(2)(0)=λ24λ+3\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

1λ203λ=(λ3)(λ1)\left|\begin{array}{cc}1 - \lambda & 2\\0 & 3 - \lambda\end{array}\right| = \left(\lambda - 3\right) \left(\lambda - 1\right)A