Question

The system of equations

            ax + ayz = 0

            bxy + bz = 0

         – x + cy + cz = 0

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

          

Solution

Correct option is

2

     

Apply C2 → C2 – C1 and C3 → C3 – C1 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

Q1

               

Q2

                    

Q3

                 

Q6

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

           

Q7

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

Q8

The system of equation

              ax + by + (aα + b)z = 0

               bx + cy + (bα + c)z = 0

            (aα + b)x + (bα + c)y = 0

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

Q9

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

                 λx + λy + z = 0

has a non – trivial solution is (are)

Q10

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

(λ + 3)x + (λ + 2)y + z = 0

        3x + (λ + 3)y + z = 0

                 2x + 3y + z = 0

has a non – trivial solution is