Solve Equations x+y+z=3,2x-y-z=3,x-y+z=9 using Gauss-Jordan Elimination methodSolution:Total Equations are `3`
`x+y+z=3 -> (1)`
`2x-y-z=3 -> (2)`
`x-y+z=9 -> (3)`
Converting given equations into matrix form
| `1` | `1` | `1` | | `3` | |
| `2` | `-1` | `-1` | | `3` | |
| `1` | `-1` | `1` | | `9` | |
`R_2 larr R_2-2xx R_1`
= | | `1` | `1` | `1` | | `3` | | | `0` | `-3` | `-3` | | `-3` | | | `1` | `-1` | `1` | | `9` | |
|
`R_3 larr R_3- R_1`
= | | `1` | `1` | `1` | | `3` | | | `0` | `-3` | `-3` | | `-3` | | | `0` | `-2` | `0` | | `6` | |
|
`R_2 larr R_2-:-3`
= | | `1` | `1` | `1` | | `3` | | | `0` | `1` | `1` | | `1` | | | `0` | `-2` | `0` | | `6` | |
|
`R_1 larr R_1- R_2`
= | | `1` | `0` | `0` | | `2` | | | `0` | `1` | `1` | | `1` | | | `0` | `-2` | `0` | | `6` | |
|
`R_3 larr R_3+2xx R_2`
= | | `1` | `0` | `0` | | `2` | | | `0` | `1` | `1` | | `1` | | | `0` | `0` | `2` | | `8` | |
|
`R_3 larr R_3-:2`
= | | `1` | `0` | `0` | | `2` | | | `0` | `1` | `1` | | `1` | | | `0` | `0` | `1` | | `4` | |
|
`R_2 larr R_2- R_3`
= | | `1` | `0` | `0` | | `2` | | | `0` | `1` | `0` | | `-3` | | | `0` | `0` | `1` | | `4` | |
|
`i.e.`
`x=2`
`y=-3`
`z=4`
Solution By Gauss jordan elimination method
`x=2,y=-3 and z=4`
This material is intended as a summary. Use your textbook for detail explanation.
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