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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
1. Definition and Examples
(Previous example)		4. Power of a matrix
(Next method)

2. Example-2


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

Solution:
`|B|` = 
 `2`  `1`  `-1` 
 `1`  `0`  `-1` 
 `1`  `1`  `2` 


 =
 `2` × 
 `0`  `-1` 
 `1`  `2` 
 `-1` × 
 `1`  `-1` 
 `1`  `2` 
 `-1` × 
 `1`  `0` 
 `1`  `1` 


`=2 xx (0 × 2 - (-1) × 1) -1 xx (1 × 2 - (-1) × 1) -1 xx (1 × 1 - 0 × 1)`

`=2 xx (0 +1) -1 xx (2 +1) -1 xx (1 +0)`

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

`= 2 -3 -1`

`=-2`


`Adj(B)` = 
Adj
`2``1``-1`
`1``0``-1`
`1``1``2`


 = 
 + 
 `0`  `-1` 
 `1`  `2` 
 - 
 `1`  `-1` 
 `1`  `2` 
 + 
 `1`  `0` 
 `1`  `1` 
 - 
 `1`  `-1` 
 `1`  `2` 
 + 
 `2`  `-1` 
 `1`  `2` 
 - 
 `2`  `1` 
 `1`  `1` 
 + 
 `1`  `-1` 
 `0`  `-1` 
 - 
 `2`  `-1` 
 `1`  `-1` 
 + 
 `2`  `1` 
 `1`  `0` 
T


 = 
`+(0 × 2 - (-1) × 1)``-(1 × 2 - (-1) × 1)``+(1 × 1 - 0 × 1)`
`-(1 × 2 - (-1) × 1)``+(2 × 2 - (-1) × 1)``-(2 × 1 - 1 × 1)`
`+(1 × (-1) - (-1) × 0)``-(2 × (-1) - (-1) × 1)``+(2 × 0 - 1 × 1)`
T


 = 
`+(0 +1)``-(2 +1)``+(1 +0)`
`-(2 +1)``+(4 +1)``-(2 -1)`
`+(-1 +0)``-(-2 +1)``+(0 -1)`
T


 = 
`1``-3``1`
`-3``5``-1`
`-1``1``-1`
T


 = 
`1``-3``-1`
`-3``5``1`
`1``-1``-1`


`"Now, "B^(-1)=1/|B| × Adj(B)`

 = `1/(-2)` ×
`1``-3``-1`
`-3``5``1`
`1``-1``-1`


 = 
`-0.5``1.5``0.5`
`1.5``-2.5``-0.5`
`-0.5``0.5``0.5`


`A×(B^(-1))`=
`2``3``1`
`0``5``6`
`1``1``2`
×
`-0.5``1.5``0.5`
`1.5``-2.5``-0.5`
`-0.5``0.5``0.5`


=
`2×-0.5+3×1.5+1×-0.5``2×1.5+3×-2.5+1×0.5``2×0.5+3×-0.5+1×0.5`
`0×-0.5+5×1.5+6×-0.5``0×1.5+5×-2.5+6×0.5``0×0.5+5×-0.5+6×0.5`
`1×-0.5+1×1.5+2×-0.5``1×1.5+1×-2.5+2×0.5``1×0.5+1×-0.5+2×0.5`


=
`-1+4.5-0.5``3-7.5+0.5``1-1.5+0.5`
`0+7.5-3``0-12.5+3``0-2.5+3`
`-0.5+1.5-1``1.5-2.5+1``0.5-0.5+1`


=
`3``-4``0`
`4.5``-9.5``0.5`
`0``0``1`


This material is intended as a summary. Use your textbook for detail explanation.
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1. Definition and Examples
(Previous example)		4. Power of a matrix
(Next method)


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