The determinant of 0 2 0 1 3 0 3 0 0 2 3 0 3 0 0 3 is Soluti

The determinant of [0 -2 0 -1 -3 0 -3 0 0 2 3 0 -3 0 0 -3] is

Solution

Determination of 4×4 matrix is calculated simply by taking sum of the first row elements multiples to their corresponding determinant matrix.

0×d1 +2×d2+0×d3+1×d4=2d2+d4

Where d2 matrix is= -3 -3 0

0 3 0

-3 0 -3

D2=-3{(3×-3) -(0×0)}+3×{(-3×0)-(-3×0)}+0{(0×0)-(-3×3)}

=-3×-9 +3×0 +0×9=27

similarly D4 matrix is -3 0 -3

0 2 3

-3 0 0

So d4 =-3×{(2×0)-(0×3)}-0×{(0×0)-(-3×3)}-3{(0×0)-(-3×2)}=-3×6=-18

So determinant=2d2+d4=2×27 -18=36