﻿ 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            : Kaysons Education

# 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

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## Question

### 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

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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