Question 245750: Find all values of k, for which the system of equations
2x-2y+kz=0
x+4z=0
kx+y+z=0
has a nonzero solution (that is, (x,y,z) not equal to (0,0,0)
Dont know this please help
Answer by TheProdicalSon(34)   (Show Source):
You can put this solution on YOUR website! Here, I don't have much time, and these kinds of problems take a lot of work to right down. So I'm just going to solve it, the work isn't going to make much sense so just look at the answer at the bottom.
2x - 2y + kz = 0
x + 4z = 0
kx + y + z = 0
x + y + z = 0
2x - 2y - z
3x - y = 0
4x 4y 4z
-x - 4z
3x 4y
6x = y
x = 0
y = 0
z = 0
okay then, I think you interpreted the question wrong, no matter how you work it out x, y, and z all equal 0.
However,
k is not a zero
k = All real numbers, infinite solutions
If this was helpful comment on my page.
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