Determinant of [4578]\left[\begin{array}{cc}4 & 5\\7 & 8\end{array}\right]

The calculator will find the determinant of the square 22x22 matrix [4578]\left[\begin{array}{cc}4 & 5\\7 & 8\end{array}\right], with steps shown.

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A

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Your Input

Calculate 4578\left|\begin{array}{cc}4 & 5\\7 & 8\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.

4578=(4)(8)(5)(7)=3\left|\begin{array}{cc}4 & 5\\7 & 8\end{array}\right| = \left(4\right)\cdot \left(8\right) - \left(5\right)\cdot \left(7\right) = -3

Answer

4578=3\left|\begin{array}{cc}4 & 5\\7 & 8\end{array}\right| = -3A