Matrix Division Definition and Examples

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3. Matrix Division example ( Enter your problem )

( Enter your problem )

Definition and Examples
Example-2

Other related methods

2. Multiplication of two matrix
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2. Example-2
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1. Definition and Examples

1. Division of matrix

1. `A/B=A*B^-1`
2. `B/A=B*A^-1`

Examples
1. Find `B/A` ...
`A=[[2,3,1],[0,5,6],[1,1,2]]`,`B=[[2,1,-1],[1,0,-1],[1,1,2]]`

Solution:

`|A|`

`2`	`3`	`1`
`0`	`5`	`6`
`1`	`1`	`2`

`2`

	`5`	`6`
	`1`	`2`

`-3`

	`0`	`6`
	`1`	`2`

`+1`

	`0`	`5`
	`1`	`1`

`=2 xx (5 × 2 - 6 × 1) -3 xx (0 × 2 - 6 × 1) +1 xx (0 × 1 - 5 × 1)`

`=2 xx (10 -6) -3 xx (0 -6) +1 xx (0 -5)`

`=2 xx (4) -3 xx (-6) +1 xx (-5)`

`= 8 +18 -5`

`=21`

`Adj(A)`

Adj

`2`	`3`	`1`
`0`	`5`	`6`
`1`	`1`	`2`

	`5`	`6`
	`1`	`2`

	`0`	`6`
	`1`	`2`

	`0`	`5`
	`1`	`1`

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

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

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

	`3`	`1`
	`5`	`6`

	`2`	`1`
	`0`	`6`

	`2`	`3`
	`0`	`5`

`+(5 × 2 - 6 × 1)`	`-(0 × 2 - 6 × 1)`	`+(0 × 1 - 5 × 1)`
`-(3 × 2 - 1 × 1)`	`+(2 × 2 - 1 × 1)`	`-(2 × 1 - 3 × 1)`
`+(3 × 6 - 1 × 5)`	`-(2 × 6 - 1 × 0)`	`+(2 × 5 - 3 × 0)`

`+(10 -6)`	`-(0 -6)`	`+(0 -5)`
`-(6 -1)`	`+(4 -1)`	`-(2 -3)`
`+(18 -5)`	`-(12 +0)`	`+(10 +0)`

`4`	`6`	`-5`
`-5`	`3`	`1`
`13`	`-12`	`10`

`4`	`-5`	`13`
`6`	`3`	`-12`
`-5`	`1`	`10`

`"Now, "A^(-1)=1/|A| × Adj(A)`

`1/(21)` ×

`4`	`-5`	`13`
`6`	`3`	`-12`
`-5`	`1`	`10`

`0.1905`	`-0.2381`	`0.619`
`0.2857`	`0.1429`	`-0.5714`
`-0.2381`	`0.0476`	`0.4762`

`B×(A^(-1))`

`2`	`1`	`-1`
`1`	`0`	`-1`
`1`	`1`	`2`

`0.1905`	`-0.2381`	`0.619`
`0.2857`	`0.1429`	`-0.5714`
`-0.2381`	`0.0476`	`0.4762`

`2×0.1905+1×0.2857-1×-0.2381`	`2×-0.2381+1×0.1429-1×0.0476`	`2×0.619+1×-0.5714-1×0.4762`
`1×0.1905+0×0.2857-1×-0.2381`	`1×-0.2381+0×0.1429-1×0.0476`	`1×0.619+0×-0.5714-1×0.4762`
`1×0.1905+1×0.2857+2×-0.2381`	`1×-0.2381+1×0.1429+2×0.0476`	`1×0.619+1×-0.5714+2×0.4762`

`0.381+0.2857+0.2381`	`-0.4762+0.1429-0.0476`	`1.2381-0.5714-0.4762`
`0.1905+0+0.2381`	`-0.2381+0-0.0476`	`0.619+0-0.4762`
`0.1905+0.2857-0.4762`	`-0.2381+0.1429+0.0952`	`0.619-0.5714+0.9524`

`0.9048`	`-0.381`	`0.1905`
`0.4286`	`-0.2857`	`0.1429`
`0`	`0`	`1`

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