The set of homogeneous equations $$tx+(t+1)y+(t$$−$$1)z=0(t+1)x+ty+(t+2)z=0(t$$−$$1)x+(t+2)y+tz=0has$$ non – trivial solutions for :

Correct option is 3one values of t

Questions

The set of homogeneous equations
$\begin{aligned} t x + (t + 1) y + (t - 1) z = 0 \\ (t + 1) x + t y + (t + 2) z = 0 \\ (t - 1) x + (t + 2) y + t z = 0 \end{aligned}$
has non – trivial solutions for :

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detailed solution

Correct option is C

tt+1t-1t+1tt+2t-1t+2t=0 R1 → R1-R2, R2 → R2-R3 -11-32-22t-1t+2t=0 -1(-2t-2t-4)-1(2t-2t+2)-3(2t+4+2t-2)=0 D simplifies to −4(2t+1)=0

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The set 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=0has non – trivial solutions for :

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Ready to Test Your Skills?

free study material

The set of homogeneous equations
$\begin{aligned} t x + (t + 1) y + (t - 1) z = 0 \\ (t + 1) x + t y + (t + 2) z = 0 \\ (t - 1) x + (t + 2) y + t z = 0 \end{aligned}$
has non – trivial solutions for :