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Problem: cofactor [[10,-9,-12],[7,-12,11],[-10,10,3]] [ Calculator, Method and examples ]

Solution:
Your problem -> cofactor [[10,-9,-12],[7,-12,11],[-10,10,3]]

COFACTOR(A) =
COFACTOR
 10 -9 -12 7 -12 11 -10 10 3

Cofactor of 10 = A_(11) =
+
 -12 11 10 3
=+((-12) × 3 - 11 × 10)=+(-36 -110)=-146

Cofactor of -9 = A_(12) =
-
 7 11 -10 3
=-(7 × 3 - 11 × (-10))=-(21 +110)=-131

Cofactor of -12 = A_(13) =
+
 7 -12 -10 10
=+(7 × 10 - (-12) × (-10))=+(70 -120)=-50

Cofactor of 7 = A_(21) =
-
 -9 -12 10 3
=-((-9) × 3 - (-12) × 10)=-(-27 +120)=-93

Cofactor of -12 = A_(22) =
+
 10 -12 -10 3
=+(10 × 3 - (-12) × (-10))=+(30 -120)=-90

Cofactor of 11 = A_(23) =
-
 10 -9 -10 10
=-(10 × 10 - (-9) × (-10))=-(100 -90)=-10

Cofactor of -10 = A_(31) =
+
 -9 -12 -12 11
=+((-9) × 11 - (-12) × (-12))=+(-99 -144)=-243

Cofactor of 10 = A_(32) =
-
 10 -12 7 11
=-(10 × 11 - (-12) × 7)=-(110 +84)=-194

Cofactor of 3 = A_(33) =
+
 10 -9 7 -12
=+(10 × (-12) - (-9) × 7)=+(-120 +63)=-57

The Cofactor matrix of A is [A_(ij)]=
 A_(11) A_(12) A_(13) A_(21) A_(22) A_(23) A_(31) A_(32) A_(33)
=
 -146 -131 -50 -93 -90 -10 -243 -194 -57

Method-2 : all Cofactors in matrix form

=
+
 -12 11 10 3
-
 7 11 -10 3
+
 7 -12 -10 10
-
 -9 -12 10 3
+
 10 -12 -10 3
-
 10 -9 -10 10
+
 -9 -12 -12 11
-
 10 -12 7 11
+
 10 -9 7 -12

=
 +((-12) × 3 - 11 × 10) -(7 × 3 - 11 × (-10)) +(7 × 10 - (-12) × (-10)) -((-9) × 3 - (-12) × 10) +(10 × 3 - (-12) × (-10)) -(10 × 10 - (-9) × (-10)) +((-9) × 11 - (-12) × (-12)) -(10 × 11 - (-12) × 7) +(10 × (-12) - (-9) × 7)

=
 +(-36 -110) -(21 +110) +(70 -120) -(-27 +120) +(30 -120) -(100 -90) +(-99 -144) -(110 +84) +(-120 +63)

=
 -146 -131 -50 -93 -90 -10 -243 -194 -57

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