1.
The number of real values of tt such that the system of homogeneous equations
tx+(t+1)y+(t1)z=0tx + (t+1)y + (t-1)z = 0

(t+1)x+ty+(t+2)z=0(t+1)x + ty + (t+2)z = 0

(t1)x+(t+2)y+tz=0(t-1)x + (t+2)y + tz = 0

has non-trivial solutions is
Matrices and Determinants - Hard - Question