Inverse of matrix using Adjoint method Example [[3,1,1],[-1,2,1],[1,1,1]]

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

1. Adjoint method example ( Enter your problem )

( Enter your problem )

Example `[[3,1,1],[-1,2,1],[1,1,1]]`
Example `[[2,3,1],[0,5,6],[1,1,2]]`
Example `[[2,3],[4,10]]`
Example `[[5,1],[4,2]]`

Other related methods

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

1. Example `[[3,1,1],[-1,2,1],[1,1,1]]`

Find Inverse of matrix
`A=[[3,1,1],[-1,2,1],[1,1,1]]`

Solution:

`|A|`

`3`	`1`	`1`
`-1`	`2`	`1`
`1`	`1`	`1`

`3`

	`2`	`1`
	`1`	`1`

`-1`

	`-1`	`1`
	`1`	`1`

`+1`

	`-1`	`2`
	`1`	`1`

`=3 xx (2 × 1 - 1 × 1) -1 xx (-1 × 1 - 1 × 1) +1 xx (-1 × 1 - 2 × 1)`

`=3 xx (2 -1) -1 xx (-1 -1) +1 xx (-1 -2)`

`=3 xx (1) - -1 xx (-2) +1 xx (-3)`

`= 3 +2 -3`

`=2`

`Adj(A)`

Adj

`3`	`1`	`1`
`-1`	`2`	`1`
`1`	`1`	`1`

	`2`	`1`
	`1`	`1`

	`-1`	`1`
	`1`	`1`

	`-1`	`2`
	`1`	`1`

	`1`	`1`
	`1`	`1`

	`3`	`1`
	`1`	`1`

	`3`	`1`
	`1`	`1`

	`1`	`1`
	`2`	`1`

	`3`	`1`
	`-1`	`1`

	`3`	`1`
	`-1`	`2`

`+(2 × 1 - 1 × 1)`	`-(-1 × 1 - 1 × 1)`	`+(-1 × 1 - 2 × 1)`
`-(1 × 1 - 1 × 1)`	`+(3 × 1 - 1 × 1)`	`-(3 × 1 - 1 × 1)`
`+(1 × 1 - 1 × 2)`	`-(3 × 1 - 1 × (-1))`	`+(3 × 2 - 1 × (-1))`

`+(2 -1)`	`-(-1 -1)`	`+(-1 -2)`
`-(1 -1)`	`+(3 -1)`	`-(3 -1)`
`+(1 -2)`	`-(3 +1)`	`+(6 +1)`

`1`	`2`	`-3`
`0`	`2`	`-2`
`-1`	`-4`	`7`

`1`	`0`	`-1`
`2`	`2`	`-4`
`-3`	`-2`	`7`

`"Now, "A^(-1)=1/|A| × Adj(A)`

`1/(2)` ×

`1`	`0`	`-1`
`2`	`2`	`-4`
`-3`	`-2`	`7`

`1/2`	`0`	`-1/2`
`1`	`1`	`-2`
`-3/2`	`-1`	`7/2`

This material is intended as a summary. Use your textbook for detail explanation.
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