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Home > Matrix & Vector calculators > Minor of a matrix example
10. Matrix Minors example ( Enter your problem )
( Enter your problem )
  1. Definition and Examples
  2. Example-2
 		Other related methods
  1. Addition of two matrix
  2. Multiplication of two matrix
  3. Division of two matrix
  4. Power of a matrix
  5. Transpose of a matrix
  6. Determinant of a matrix
  7. Adjoint of a matrix
  8. Inverse of a matrix
  9. Prove that any two matrix expression is equal or not
  10. Minor of a matrix
  11. Cofactor of a matrix
  12. Trace of a matrix
1. Definition and Examples
(Previous example)		11. Cofactor of a matrix
(Next method)

2. Example-2


1. Find `"Minor"(A)` ...
`A=[[1,2],[4,5]]`

Solution:
`MINOR(A)` = 
`MINOR`
`1``2`
`4``5`


`A_(11)=`minor of `1=`
 `5` 
`=5``=5`


`A_(12)=`minor of `2=`
 `4` 
`=4``=4`


`A_(21)=`minor of `4=`
 `2` 
`=2``=2`


`A_(22)=`minor of `5=`
 `1` 
`=1``=1`


The minor matrix of A is `[A_(ij)]`=
`A_(11)``A_(12)`
`A_(21)``A_(22)`
=
`5``4`
`2``1`


Method-2 : all minors in matrix form

=
 `5` 
 `4` 
 `2` 
 `1` 


=
`5``4`
`2``1`
2. Find `"Minor"(A)` ...
`A=[[1,2,3],[4,5,6],[7,8,9]]`

Solution:
`MINOR(A)` = 
`MINOR`
`1``2``3`
`4``5``6`
`7``8``9`


`A_(11)=`minor of `1=`
 `5`  `6` 
 `8`  `9` 
`=5 × 9 - 6 × 8``=45 -48``=-3`


`A_(12)=`minor of `2=`
 `4`  `6` 
 `7`  `9` 
`=4 × 9 - 6 × 7``=36 -42``=-6`


`A_(13)=`minor of `3=`
 `4`  `5` 
 `7`  `8` 
`=4 × 8 - 5 × 7``=32 -35``=-3`


`A_(21)=`minor of `4=`
 `2`  `3` 
 `8`  `9` 
`=2 × 9 - 3 × 8``=18 -24``=-6`


`A_(22)=`minor of `5=`
 `1`  `3` 
 `7`  `9` 
`=1 × 9 - 3 × 7``=9 -21``=-12`


`A_(23)=`minor of `6=`
 `1`  `2` 
 `7`  `8` 
`=1 × 8 - 2 × 7``=8 -14``=-6`


`A_(31)=`minor of `7=`
 `2`  `3` 
 `5`  `6` 
`=2 × 6 - 3 × 5``=12 -15``=-3`


`A_(32)=`minor of `8=`
 `1`  `3` 
 `4`  `6` 
`=1 × 6 - 3 × 4``=6 -12``=-6`


`A_(33)=`minor of `9=`
 `1`  `2` 
 `4`  `5` 
`=1 × 5 - 2 × 4``=5 -8``=-3`


The minor matrix of A is `[A_(ij)]`=
`A_(11)``A_(12)``A_(13)`
`A_(21)``A_(22)``A_(23)`
`A_(31)``A_(32)``A_(33)`
=
`-3``-6``-3`
`-6``-12``-6`
`-3``-6``-3`


Method-2 : all minors in matrix form

=
 `5`  `6` 
 `8`  `9` 
 `4`  `6` 
 `7`  `9` 
 `4`  `5` 
 `7`  `8` 
 `2`  `3` 
 `8`  `9` 
 `1`  `3` 
 `7`  `9` 
 `1`  `2` 
 `7`  `8` 
 `2`  `3` 
 `5`  `6` 
 `1`  `3` 
 `4`  `6` 
 `1`  `2` 
 `4`  `5` 


=
`5 × 9 - 6 × 8``4 × 9 - 6 × 7``4 × 8 - 5 × 7`
`2 × 9 - 3 × 8``1 × 9 - 3 × 7``1 × 8 - 2 × 7`
`2 × 6 - 3 × 5``1 × 6 - 3 × 4``1 × 5 - 2 × 4`


=
`45 -48``36 -42``32 -35`
`18 -24``9 -21``8 -14`
`12 -15``6 -12``5 -8`


=
`-3``-6``-3`
`-6``-12``-6`
`-3``-6``-3`


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1. Definition and Examples
(Previous example)		11. Cofactor of a matrix
(Next method)


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