SOLUTION: what condition a &b must satisfy so that the following system has nontrival solution? x+y+ax=0 x+y+bz=0 ax+by+z=0

Question 1044650: what condition a &b must satisfy so that the following system has nontrival
solution?
x+y+ax=0
x+y+bz=0
ax+by+z=0

Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
I will assume that your first equation is actually x+y+az = 0.
Simply equate the determinant of the coefficient matrix to 0:

===>
===>
===> , for the system to have a non-trivial solution.
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!

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