Question 389348: find the value of the determinant.
1 4 7
-2 5 2
2 5 -2
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 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
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