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Home > Matrix & Vector calculators > Inverse of matrix using Gauss-Jordan Elimination method example
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2. Gauss-Jordan Elimination 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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2. Example `[[2,3,1],[0,5,6],[1,1,2]]`
(Previous example) | 4. Example `[[5,1],[4,2]]`
(Next example) |
3. Example `[[2,3],[4,10]]`
3. Find Inverse of matrix using Gauss-Jordan Elimination method
`A=[[2,3],[4,10]]`
Solution:
Given matrix is
Now finding inverse of the given matrix
| `2` | `3` | | `1` | `0` | | | `4` | `10` | | `0` | `1` | |
`R_1 larr R_1-:2`
| = | | `1` | `(3)/2` | | `(1)/2` | `0` | | | `4` | `10` | | `0` | `1` | |
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`R_2 larr R_2-4xx R_1`
| = | | `1` | `(3)/2` | | `(1)/2` | `0` | | | `0` | `4` | | `-2` | `1` | |
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`R_2 larr R_2-:4`
| = | | `1` | `(3)/2` | | `(1)/2` | `0` | | | `0` | `1` | | `(-1)/2` | `(1)/4` | |
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`R_1 larr R_1-(3)/2xx R_2`
| = | | `1` | `0` | | `(5)/4` | `(-3)/8` | | | `0` | `1` | | `(-1)/2` | `(1)/4` | |
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Solution By Gauss Elimination Method
`[[(5)/4,(-3)/8],[(-1)/2,(1)/4]]`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
2. Example `[[2,3,1],[0,5,6],[1,1,2]]`
(Previous example) | 4. Example `[[5,1],[4,2]]`
(Next example) |
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