SOLUTION: Find the number of real values of C for which the following system of equations has infinite number of solution: x + 3y + 5z = Cx 5x + y + 3z = Cy 3x + 5y + z = Cz

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Question 1184298: Find the number of real values of C for which the following system of equations has infinite number of solution:
x + 3y + 5z = Cx
5x + y + 3z = Cy
3x + 5y + z = Cz
Found 2 solutions by ikleyn, robertb:
Answer by ikleyn(52864) About Me  (Show Source):
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The system is the same as
(1-c)x + 3y + 5z=0
5x + (1-c)y + 3z=0
3x + 5y + (1-c)z =0
Now let abs%28matrix%283%2C3%2C1-c%2C+3%2C5%2C5%2C1-c%2C3%2C3%2C5%2C1-c%29%29=0
===> 108%2B42c%2B3c%5E2-c%5E3=0 ===> c = 9. (Other roots are complex.)
Therefore the system will have an infinite number of solutions if highlight%28c=9%29.