Inverse matrix Example-2

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Home > Matrix & Vector calculators > Inverse of a matrix example

8. Inverse matrix example ( Enter your problem )

( Enter your problem )

Definition and Examples
Example-2

Other related methods

1. Definition and Examples
(Previous example)

9. Prove that any two matrix expression is equal or not
(Next method)

2. Example-2

1. Find `A^-1` ...
`A=[[1,2],[4,5]]`

Solution:

`|A|`

	`1`	`2`
	`4`	`5`

`=1 × 5 - 2 × 4`

`=5 -8`

`=-3`

`Adj(A)`

Adj

	`1`	`2`
	`4`	`5`

	`+(5)`	`-(4)`
	`-(2)`	`+(1)`

	`5`	`-4`
	`-2`	`1`

	`5`	`-2`
	`-4`	`1`

`"Now, "A^(-1)=1/|A| × Adj(A)`

`1/(-3)` ×

	`5`	`-2`
	`-4`	`1`

	`-1.6667`	`0.6667`
	`1.3333`	`-0.3333`

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

Solution:

`|A|`

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

`1`

	`5`	`6`
	`8`	`9`

`-2`

	`4`	`6`
	`7`	`9`

`+3`

	`4`	`5`
	`7`	`8`

`=1 xx (5 × 9 - 6 × 8) -2 xx (4 × 9 - 6 × 7) +3 xx (4 × 8 - 5 × 7)`

`=1 xx (45 -48) -2 xx (36 -42) +3 xx (32 -35)`

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

`= -3 +12 -9`

`=0`

`Here, |A|=0, " So " (A)^(-1)" is not possible."`

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