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Definition and examples
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Matrix operations
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Matrix Operation
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Matrix Division calculator |
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Matrix A :
X
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- `[[1,0,0],[0,1,0],[0,0,1]]`
- `[[2,3,1],[0,5,6],[1,1,2]]`
- `[[2,1,-1],[1,0,-1],[1,1,2]]`
- `[[3,1,1],[-1,2,1],[1,1,1]]`
- `[[5,6,1],[0,2,3],[1,1,2]]`
- `[[5,-1,1],[-2,3,4],[1,1,7]]`
- `[[2,3,-1],[3,2,1],[1,-5,3]]`
- `[[1,1,1],[2,-1,-1],[1,-1,1]]`
- `[[1,1,1],[1,2,3],[1,4,9]]`
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Matrix B :
X
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- `[[1,0,0],[0,1,0],[0,0,1]]`
- `[[2,3,1],[0,5,6],[1,1,2]]`
- `[[2,1,-1],[1,0,-1],[1,1,2]]`
- `[[3,1,1],[-1,2,1],[1,1,1]]`
- `[[5,6,1],[0,2,3],[1,1,2]]`
- `[[5,-1,1],[-2,3,4],[1,1,7]]`
- `[[2,3,-1],[3,2,1],[1,-5,3]]`
- `[[1,1,1],[2,-1,-1],[1,-1,1]]`
- `[[1,1,1],[1,2,3],[1,4,9]]`
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Matrix C :
X
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- `[[1,0,0],[0,1,0],[0,0,1]]`
- `[[2,3,1],[0,5,6],[1,1,2]]`
- `[[2,1,-1],[1,0,-1],[1,1,2]]`
- `[[3,1,1],[-1,2,1],[1,1,1]]`
- `[[5,6,1],[0,2,3],[1,1,2]]`
- `[[5,-1,1],[-2,3,4],[1,1,7]]`
- `[[2,3,-1],[3,2,1],[1,-5,3]]`
- `[[1,1,1],[2,-1,-1],[1,-1,1]]`
- `[[1,1,1],[1,2,3],[1,4,9]]`
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Mode =
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Decimal Place =
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To solve simultaneous equations, enter B/A or AX=B or Use this link
Inverse Matrix method (for answer in better way)
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Solution
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Solution provided by AtoZmath.com
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Matrix Division calculator
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1. `A=[[2,3,1],[0,5,6],[1,1,2]]` and `B=[[2,1,-1],[1,0,-1],[1,1,2]]`. Find A/B 2. `A=[[2,3,1],[0,5,6],[1,1,2]]` and `B=[[2,1,-1],[1,0,-1],[1,1,2]]`. Find B/A 3. `A=[[2,3],[4,10]]` and `B=[[5,1],[4,2]]`. Find A/B 4. `A=[[5,1],[4,2]]` and `B=[[6,3],[4,5]]`. Find B/A
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Example1. 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` | |
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`=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` | |
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= | | `+(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)` | |
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= | | `+(10 -6)` | `-(0 -6)` | `+(0 -5)` | | | `-(6 -1)` | `+(4 -1)` | `-(2 -3)` | | | `+(18 -5)` | `-(12 +0)` | `+(10 +0)` | |
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= | | `4` | `6` | `-5` | | | `-5` | `3` | `1` | | | `13` | `-12` | `10` | |
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= | | `4` | `-5` | `13` | | | `6` | `3` | `-12` | | | `-5` | `1` | `10` | |
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`"Now, "A^(-1)=1/|A| × Adj(A)` = | `1/(21)` × | | `4` | `-5` | `13` | | | `6` | `3` | `-12` | | | `-5` | `1` | `10` | |
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= | | `0.1905` | `-0.2381` | `0.619` | | | `0.2857` | `0.1429` | `-0.5714` | | | `-0.2381` | `0.0476` | `0.4762` | |
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`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` | |
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= | | `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` | |
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= | | `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` | |
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= | | `0.9048` | `-0.381` | `0.1905` | | | `0.4286` | `-0.2857` | `0.1429` | | | `0` | `0` | `1` | |
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