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Home > Matrix & Vector calculators > Adjoint of a matrix example
7. Adjoint matrix or adjugate matrix 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)		8. Inverse of a matrix
(Next method)

2. Example-2


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

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


 = 
`+(5)``-(4)`
`-(2)``+(1)`
T


 = 
`5``-4`
`-2``1`
T


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

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


 = 
 + 
 `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` 
T


 = 
`+(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)`
T


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


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


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


This material is intended as a summary. Use your textbook for detail explanation.
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1. Definition and Examples
(Previous example)		8. Inverse of a matrix
(Next method)


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