Homework SourseSolve the following linear system 2a 5b 8c 2d 2e 0 6a
Solve the following linear system:
2a + 5b - 8c + 2d + 2e = 0
6a + 2b - 10c + 6d + 8e = 6
3a + 6b + 2c + 3d + 5e = 6
3a + 1b - 5c + 3d + 4e = 3
6a + 7b - 3c + 6d + 9e = 9
Please use Gaussian Elimination and it wil be great if you explain with augmented matrix. Thank you!
Solution
It can have infinite number of solution. Number of equation is > number of variables.
| a | b | c | d | e | |
| 2 | 5 | -8 | 2 | 2 | 0 |
| 6 | 2 | -10 | 6 | 8 | 6 |
| 3 | 6 | 2 | 3 | 5 | 6 |
| 3 | 1 | -5 | 3 | 4 | 3 |
| 6 | 7 | -3 | 6 | 9 | 9 |
| a | b | c | d | e | 0 |
| 2 | 5 | -8 | 2 | 2 | 0 |
| 0 | -13 | 14 | 0 | 2 | 6 |
| 0 | 5 | 7 | 0 | 1 | 3 |
| 0 | -5 | -7 | 0 | -1 | -3 |
| 0 | 5 | 7 | 0 | 1 | 3 |
| a | b | c | d | e | 0 |
| 2 | 0 | -2.61538 | 2 | 2.769231 | 2.307692 |
| 0 | 1 | -1.07692 | 0 | -0.15385 | -0.46154 |
| 0 | 0 | 12.38462 | 0 | 1.769231 | 5.307692 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| a | b | c | d | e | |
| 26 | 0 | -34 | 26 | 36 | 30 |
| 0 | 13 | -14 | 0 | -2 | -6 |
| 0 | 0 | 161 | 0 | 23 | 69 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 |
