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Find cofactor [[10,-9,-12],[7,-12,11],[-10,10,3]]

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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