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Home > Matrix & Vector calculators > Division of two matrix example
3. Matrix Division example ( Enter your problem )
( Enter your problem )
  1. Definition and Examples
  2. Example-2
 		Other related methods
  1. Addition of two matrix
  2. Multiplication of two matrix
  3. Division of two matrix
  4. Power of a matrix
  5. Transpose of a matrix
  6. Determinant of a matrix
  7. Adjoint of a matrix
  8. Inverse of a matrix
  9. Prove that any two matrix expression is equal or not
  10. Minor of a matrix
  11. Cofactor of a matrix
  12. Trace of a matrix
2. Multiplication of two matrix
(Previous method)		2. Example-2
(Next example)

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` 
T


 = 
`+(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)`
T


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


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


 = 
`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`


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2. Multiplication of two matrix
(Previous method)		2. Example-2
(Next example)


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