Question

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20

Answer 1

Double the first equation:
8x - 2y + 6x = 24
Subtract the second equation from that:
7x - 6y = 56
Triple the first equation:
12x - 3y + 9z = 36
Subtract the third equation from that:
7x - 6y = 16
That's a contradiction.
No solution.

Answer 2

im sorry i dont know if i understand that... so the answer is no solution? how does doubling and tripling the equation prove that its a contradiction?

Answer 3

@MaddieLB

Answer 4

so by doubling the eqaution and subtracting the 2nd and the tripling and subtracting the third we should have the same result? yes?

Answer 5

Yes

Answer 6

is that gaussian elimination though?

Answer 7

Yes, here is another look at it a different way
4 | -1 | 3 | 12 |
1 | 4 | 6 | -32 |
5 | 3 | 9 | 20 |
------------------
1 | -0.25 | 0.75 | 3 |
0 | 4.25 | 5.25 | -35 |
0 | 4.25 | 5.25 | 5 |
------------------
1 | -0.25 | 0.75 | 3 |
0 | 1 | 1.2353 | -8.2353 |
0 | 0 | 0 | 40 |

∅

Answer 8

Alright hope that helped, I gotta go

Answer 9

@nthenic_oftime do you understand?

Answer 10

im not sure... the matricies he gave me... idk how that is relating to my equations... the first one yeah i got that but idk how the other two are the same as doubling and trippling the first one... :(

Answer 11

@AloneS