Home > Matrix & Vector calculators > Inverse of matrix using Adjoint method example

1. Adjoint method example ( Enter your problem )
  1. Example `[[3,1,1],[-1,2,1],[1,1,1]]`
  2. Example `[[2,3,1],[0,5,6],[1,1,2]]`
  3. Example `[[2,3],[4,10]]`
  4. Example `[[5,1],[4,2]]`
Other related methods
  1. Adjoint method
  2. Gauss-Jordan Elimination method
  3. Cayley Hamilton method

3. Example `[[2,3],[4,10]]`
(Previous example)
2. Gauss-Jordan Elimination method
(Next method)

4. Example `[[5,1],[4,2]]`





Find Inverse of matrix
`A=[[5,1],[4,2]]`


Solution:
`|A|` = 
 `5`  `1` 
 `4`  `2` 


`=5 × 2 - 1 × 4`

`=10 -4`

`=6`


`Adj(A)` = 
Adj
`5``1`
`4``2`


 = 
`+(2)``-(4)`
`-(1)``+(5)`
T


 = 
`2``-4`
`-1``5`
T


 = 
`2``-1`
`-4``5`


`"Now, "A^(-1)=1/|A| × Adj(A)`

 = `1/(6)` ×
`2``-1`
`-4``5`


 = 
`0.3333``-0.1667`
`-0.6667``0.8333`



This material is intended as a summary. Use your textbook for detail explanation.
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3. Example `[[2,3],[4,10]]`
(Previous example)
2. Gauss-Jordan Elimination method
(Next method)





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