SOLUTION: Find the value(s) of "k" so that the system is inconsistent: x + y + 3z = 1 x + ky + 3z = 1 x + 2y + kz = 3

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Find the value(s) of "k" so that the system is inconsistent: x + y + 3z = 1 x + ky + 3z = 1 x + 2y + kz = 3      Log On


   

Question 1031677: Find the value(s) of "k" so that the system is inconsistent:
x + y + 3z = 1
x + ky + 3z = 1
x + 2y + kz = 3
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the determinant in terms of k.
D=1%28k%5E2-6%29%2B1%283-k%29%2B3%282-k%29
D=k%5E2-6%2B3-3k%2B6-2k
D=k%5E2-4k%2B3
D=%28k-3%29%28k-1%29
When k=1, the system becomes dependent since rows 1 and 2 are identical.
When k=3, the system becomes inconsistent.