The system of homogeneous equations
tx + (t + 1)y + (t – 1)z = 0
(t + 1)2 + ty + (t + 2)z = 0
(t - 1)r + (t + 2)y + tz = 0
has non-trivial solutions for
(a) exactly three real values of t
(b) exactly two real values of t
(c) exactly one real value of t
(d) infinite number of values of t
Answers
Answered by
1
Answer:
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 for
share
Share
Answer
Correct option is
C
exactly one real value of t
For the system of equations to have non-trivial solution,
Δ=
⎣
⎢
⎢
⎡
t
t+1
t−1
t+1
t
t+2
t−1
t+2
t
⎦
⎥
⎥
⎤
=0
Applying C
2
→C
2
−C
1
,C
3
→C
3
−C
1
,
we get
Δ=
⎣
⎢
⎢
⎡
t
t+1
t−1
1
−1
3
−1
1
1
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
2t+1
t+1
t−1
0
−1
3
0
1
1
⎦
⎥
⎥
⎤
(using R
1
→R
1
+R
2
)
=(2t+1)(−4)=0⇒t=
2
−1
Hence, option C.
Similar questions