Hello,

I have the linear system of presumably 3 variables ( the book does not say):

$\displaystyle x+ay=0$

$\displaystyle y+bz=0$

$\displaystyle z+cx=0$

We are asked:

In the answer, they claim that for $\displaystyle abc\neq-1$ there is a unique solution and so for $\displaystyle abc=-1$ there is are infinitely many solutions.Find (if possible) conditions a,b,c such that the system has infinitely many solutions, no solutions or one solution.

My question is, how did they find the base case abc=-1?

Thank you,

-Sakon