The value of λ for which the system of equations (1-λ) x+3 y-4 z=0 x-(3+λ) y+5 z=0 3 x+y-λ z=0 possesses non-trivial solutions is(are)

Question

The value of λ for which the system of equations (1-λ) x+3 y-4 z=0 x-(3+λ) y+5 z=0 3 x+y-λ z=0 possesses non-trivial solutions is(are) (A) -1 (B) 0 (C) 1 (D) 2

Tardigrade Admin · Accepted Answer

Put |(1-λ) 3 -4 1 -(3+λ) 5 3 1 -λ|=0 ⇒ λ(λ+1)2=0 ⇒ λ=-1,0

Q. The value of $λ$ for which the system of equations
$(1 - λ) x + 3 y - 4 z = 0$
$x - (3 + λ) y + 5 z = 0$
$3 x + y - λ z = 0$
possesses non-trivial solutions is(are)

-1

0

1

2

Put $∣ ∣ (1 - λ) 13 3 - (3 + λ) 1 - 4 5 - λ ∣ ∣ = 0$
$\Rightarrow λ (λ + 1)^{2} = 0 \Rightarrow λ = - 1, 0$

Q. The value of λ for which the system of equations (1−λ)x+3y−4z=0 x−(3+λ)y+5z=0 3x+y−λz=0 possesses non-trivial solutions is(are)

-1

0

1

2

Put ∣∣​(1−λ)13​3−(3+λ)1​−45−λ​∣∣​=0 ⇒λ(λ+1)2=0⇒λ=−1,0

Q. The value of $λ$ for which the system of equations
$(1 - λ) x + 3 y - 4 z = 0$
$x - (3 + λ) y + 5 z = 0$
$3 x + y - λ z = 0$
possesses non-trivial solutions is(are)

Put $∣ ∣ (1 - λ) 13 3 - (3 + λ) 1 - 4 5 - λ ∣ ∣ = 0$
$\Rightarrow λ (λ + 1)^{2} = 0 \Rightarrow λ = - 1, 0$