The number of real values of $t$ such that the system of homogeneous equations:\[tx+(t+1)y+(t-1)z=0\]\[(t+1)x+ty+(t+2)z=0\] \[(t-1)x+(t+2)y+tz=0\] has non-trivial solutions, is - Clay6.com, a Free resource for your JEE, AIPMT and Board Exam preparation

The number of real values of $t$ such that the system of homogeneous equations:\[tx+(t+1)y+(t-1)z=0\]\[(t+1)x+ty+(t+2)z=0\] \[(t-1)x+(t+2)y+tz=0\] has non-trivial solutions, is