The system of equations 3x - 2y+z=0, λ x -14y+ 15z=0, x + 2y-3z = 0 has a solution other than x=y = z = 0, then λ is equal to

Question

The system of equations 3x - 2y+z=0, λ x -14y+ 15z=0, x + 2y-3z = 0 has a solution other than x=y = z = 0, then λ is equal to (A) 1 (B) 2 (C) 3 (D) 5

Tardigrade Admin · Accepted Answer

The system of equations has infinitely many(non-trivial) solutions, i.e. Δ = 0. ⇒ | beginmatrix3&-2&1 λ&-14&15 1&2&-3 endmatrix|=0 ⇒ 3(42-30)-λ(6-2)+1(-30+14)=0 ⇒ 36-4λ - 16 = 0 ⇒ λ= 5

Q. The system of equations $3 x - 2 y + z = 0$ , $λ x - 14 y + 15 z = 0$ , $x + 2 y - 3 z = 0$ has a solution other than $x = y = z = 0$ , then $λ$ is equal to

$1$

$2$

$3$

$5$

The system of equations has infinitely many(non-trivial) solutions, i.e. $Δ = 0$ .
$\Rightarrow ∣ ∣ 3 λ 1 - 2 - 14 2 115 - 3 ∣ ∣ = 0 \Rightarrow 3 (42 - 30) - λ (6 - 2) + 1 (- 30 + 14) = 0$
$\Rightarrow 36 - 4 λ - 16 = 0 \Rightarrow λ = 5$

Q. The system of equations 3x−2y+z=0, λx−14y+15z=0, x+2y−3z=0 has a solution other than x=y=z=0, then λ is equal to

1

2

3

5

The system of equations has infinitely many(non-trivial) solutions, i.e. Δ=0. ⇒∣∣​3λ1​−2−142​115−3​∣∣​=0⇒3(42−30)−λ(6−2)+1(−30+14)=0 ⇒36−4λ−16=0⇒λ=5

Q. The system of equations $3 x - 2 y + z = 0$ , $λ x - 14 y + 15 z = 0$ , $x + 2 y - 3 z = 0$ has a solution other than $x = y = z = 0$ , then $λ$ is equal to

$1$

$2$

$3$

$5$

The system of equations has infinitely many(non-trivial) solutions, i.e. $Δ = 0$ .
$\Rightarrow ∣ ∣ 3 λ 1 - 2 - 14 2 115 - 3 ∣ ∣ = 0 \Rightarrow 3 (42 - 30) - λ (6 - 2) + 1 (- 30 + 14) = 0$
$\Rightarrow 36 - 4 λ - 16 = 0 \Rightarrow λ = 5$