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The system of homogenous equations tx+...

The system of homogenous 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 a non trivial solution for

A

exactly three real values of `t`

B

exactly two real values of `t`

C

exactly one real values of `t`

D

infinite number of values of `t`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` To have a non-trivial solution
`|{:(t,t+1,t-1),(t+1,t,t+2),(t-1,t+2,t):}|=0`
`implies2t+1=0impliest=-(1)/(2)`
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