SOLUTION: For a certain value of k, the system x+y+3z=10 -4x+2y+5z=7 kx+z=3 has no solutions. What is this value of k?

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Question 964779: For a certain value of k, the system
x+y+3z=10
-4x+2y+5z=7
kx+z=3
has no solutions. What is this value of k?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the determinant of the system and set it equal to zero,
A=%28matrix%283%2C3%2C1%2C1%2C3%2C-4%2C2%2C5%2Ck%2C0%2C1%29%29
abs%28A%29=1%282%281%29-5%280%29%29%2B1%285k%2B4%29%2B3%28-4%280%29-2k%29
abs%28A%29=6-k%29
6-k=0
highlight%28k=6%29