AP EAMCET Engineering 2013 Solved Paper

Given,
tx+(t+1)y+(t−1)z=0
(t+1)x+ty+(t+2)z=0
(t−1)x+(t+2)y+tz=0
Here,
Coefficient matrix, A=[

t	t+1	t−1
t+1	t	t+2
t−1	t+2	t

]
If |A| = 0, then system of equations has non-trivial solution and it has infinite solutions.
|A|=|

t	t+1	t−1
t+1	t	t+2
t−1	t+2	t

|
Apply operation R2→R2−R1,R3→R3−R1, we get
=|

t	t+1	t−1
1	−1	3
−1	1	1

|=0
Apply C2→C2−C1,C3→C3−C1, we get
|

t	1	−1
1	−2	2
−1	2	2

|=0
Expanding along R1, we get
(−4−4)−1(2+2)−1(2−2)=0
⇒ −8t−4=0
∴t=

−1

2

So, no option is correct.