SOLUTION: which condition must be placed on a,b,c, so that the system x+2y-3z=a 2x+6y-11z=b x-2y+7z=c is consistent ? can the system have unique solution.

Algebra ->  College  -> Linear Algebra -> SOLUTION: which condition must be placed on a,b,c, so that the system x+2y-3z=a 2x+6y-11z=b x-2y+7z=c is consistent ? can the system have unique solution.      Log On


   

Question 1042313: which condition must be placed on a,b,c, so that the system
x+2y-3z=a
2x+6y-11z=b
x-2y+7z=c
is consistent ? can the system have unique solution.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
which condition must be placed on a,b,c, so that the system
x+2y-3z=a
2x+6y-11z=b
x-2y+7z=c
is consistent ? can the system have unique solution.



-2R1+1R2->R2

matrix%283%2C1%2C-2%2C1%2C%22%22%29



-1R1+1R3->R3


matrix%283%2C1%2C-1%2C%22%22%2C1%29



2R2+1R3->R3

matrix%283%2C1%2C%22%22%2C2%2C1%29



To be consistent, since all the elements
but the last one on the bottom row are 0,
the last one must be 0 also:

2%28-2a%2Bb%29%2B%28c-a%29+=+0

-4a%2B2b%2Bc-a+=+0

-5a%2B2b%2Bc=0

Or if you prefer c = 5a-2b

There will only be a unique solution if a=b=c=0

and that unique solution will be (x,y,z) = (0,0,0)

Edwin