## Question

The system of equations

* ax* + *ay* – *z* = 0

* bx* – *y* + *bz* = 0

– *x* + *cy* + *cz* = 0

(where *a*, *b*, *c* ≠ – 1 )has a non – trivial solution, then value of

### Solution

2

Apply C_{2} → C_{2} – C_{1} and C_{3} → C_{3} – C_{1} and expand to obtain

*a*(*b* + 1) (*c* + 1) – *b*(*a* + 1) (*c* + 1) – (*a* + 1) (*b* + 1) = 0

divided by (*a* + 1) (*b* + 1) (*c* + 1) and solving we get = 2

#### SIMILAR QUESTIONS

The value of θ lying between θ = 0 and θ = π/2 and satisfying the equation

If *pqr* *≠* 0 and the system of equations

(*p* + *a*)*x* + *by* + *cz* = 0

* ax* + (*q* + *b*)*y* + *cz* = 0

* ax* + *by* + (*r* + *c*)*z* = 0

has sc non – trivial solution, then value of

The system of equation

* ax* + *by* + (*a*α + *b*)*z* = 0

* bx* + *cy* + (*b*α + *c*)*z* = 0

(*a*α + *b*)*x* + (* b*α +

__c__)

*y*= 0

has a non – zero solution if *a*, *b*, *c* are in

The values of λ for which the system of equations

(λ + 5)*x* + (λ – 4)*y* + *z* = 0

(λ – 2)*x* + (λ + 3)*y* + *z* = 0

λ*x* + λ*y* + *z* = 0

has a non – trivial solution is (are)

Number of real values of λ for which the system of equations

(λ + 3)*x* + (λ + 2)*y* + *z* = 0

3*x* + (λ + 3)*y* + *z* = 0

2*x* + 3*y* + *z* = 0

has a non – trivial solution is