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

2. Example `[[2,3,1],[0,5,6],[1,1,2]]`
(Previous example)
4. Example `[[5,1],[4,2]]`
(Next example)

3. Example `[[2,3],[4,10]]`





Find Inverse of matrix
`A=[[2,3],[4,10]]`


Solution:
`|A|` = 
 `2`  `3` 
 `4`  `10` 


`=2 × 10 - 3 × 4`

`=20 -12`

`=8`


`Adj(A)` = 
Adj
`2``3`
`4``10`


 = 
`+(10)``-(4)`
`-(3)``+(2)`
T


 = 
`10``-4`
`-3``2`
T


 = 
`10``-3`
`-4``2`


`"Now, "A^(-1)=1/|A| × Adj(A)`

 = `1/(8)` ×
`10``-3`
`-4``2`


 = 
`1.25``-0.375`
`-0.5``0.25`



This material is intended as a summary. Use your textbook for detail explanation.
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2. Example `[[2,3,1],[0,5,6],[1,1,2]]`
(Previous example)
4. Example `[[5,1],[4,2]]`
(Next example)





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