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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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4. Example `[[5,1],[4,2]]`
4. Find Inverse of matrix using Gauss-Jordan Elimination method
`A=[[5,1],[4,2]]`
Solution:
Given matrix is
Now finding inverse of the given matrix
`R_1 larr R_1-:5`
| = | | `1` | `(1)/5` | | `(1)/5` | `0` | | | `4` | `2` | | `0` | `1` | |
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`R_2 larr R_2-4xx R_1`
| = | | `1` | `(1)/5` | | `(1)/5` | `0` | | | `0` | `(6)/5` | | `(-4)/5` | `1` | |
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`R_2 larr R_2-:(6)/5`
| = | | `1` | `(1)/5` | | `(1)/5` | `0` | | | `0` | `1` | | `(-3.3333)/5` | `0.8333` | |
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`R_1 larr R_1-(1)/5xx R_2`
| = | | `1` | `0` | | `(41.6667)/125` | `(-0.8333)/5` | | | `0` | `1` | | `(-3.3333)/5` | `0.8333` | |
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Solution By Gauss Elimination Method
`[[(41.6667)/125,(-0.8333)/5],[(-3.3333)/5,0.8333]]`
This material is intended as a summary. Use your textbook for detail explanation.
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