SOLUTION: Consider the system x-2y+6z=a -x+y-z=b -3x+y+8z=c a)Determine the conditions (if any) on a, b, and c in order for the system to be consistent

Algebra ->  College  -> Linear Algebra -> SOLUTION: Consider the system x-2y+6z=a -x+y-z=b -3x+y+8z=c a)Determine the conditions (if any) on a, b, and c in order for the system to be consistent      Log On


   

Question 1030085: Consider the system
x-2y+6z=a
-x+y-z=b
-3x+y+8z=c
a)Determine the conditions (if any) on a, b, and c in order for the system to be consistent
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
There are NO conditions on a, b, c in order for the system to be consistent.
The reason is, the augmented matrix %28matrix%283%2C4%2C1%2C+-2%2C+6%2C+a%2C+-1%2C+1%2C+-1%2C+b%2C+-3%2C+1%2C+8%2C+c%29%29 is row-reducible to the matrix , which guarantees that the system will always have a solution for arbitrary values of a, b, and c.