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1. Adjoint method example
( Enter your problem )
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- Example `[[3,1,1],[-1,2,1],[1,1,1]]`
- Example `[[2,3,1],[0,5,6],[1,1,2]]`
- Example `[[2,3],[4,10]]`
- Example `[[5,1],[4,2]]`
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Other related methods
- Adjoint method
- Gauss-Jordan Elimination method
- Cayley Hamilton method
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1. Example `[[3,1,1],[-1,2,1],[1,1,1]]`
(Previous example) | 3. Example `[[2,3],[4,10]]`
(Next example) |
2. Example `[[2,3,1],[0,5,6],[1,1,2]]`
Find Inverse of matrix
`A=[[2,3,1],[0,5,6],[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)` | |
| T |
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| = | | `+(10 -6)` | `-(0 -6)` | `+(0 -5)` | | | `-(6 -1)` | `+(4 -1)` | `-(2 -3)` | | | `+(18 -5)` | `-(12 +0)` | `+(10 +0)` | |
| T |
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| = | | `4` | `6` | `-5` | | | `-5` | `3` | `1` | | | `13` | `-12` | `10` | |
| T |
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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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| = | | `4/21` | `-5/21` | `13/21` | | | `2/7` | `1/7` | `-4/7` | | | `-5/21` | `1/21` | `10/21` | |
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This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
1. Example `[[3,1,1],[-1,2,1],[1,1,1]]`
(Previous example) | 3. Example `[[2,3],[4,10]]`
(Next example) |
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