Question 389348
M[1,4,7:-2,5,2:2,5,-2]

Setup the determinant by breaking it into smaller components.
1M[D,5,2:5,-2]-(-2)M[D,4,7:5,-2]+2M[D,4,7:5,2]

The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb
(5)(-2)-(5)(2)-(-2)M[D,4,7:5,-2]+2M[D,4,7:5,2]

Simplify the determinant.
-20-(-2)M[D,4,7:5,-2]+2M[D,4,7:5,2]

The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb
-20-(-2)((4)(-2)-(5)(7))+2M[D,4,7:5,2]

Simplify the determinant.
-20-86+2M[D,4,7:5,2]

The determinant of a 2x2 matrix can be found using the formula M[D,a,b:c,d]=ad-cb
-20-86+2((4)(2)-(5)(7))

Simplify the determinant.
-20-86-54

Simplify the expression.
-160