The existence of the unique solution of the system x +y +z=λ, 5 x-y+μ z=10, 2 x+3 y-z=6 depends on

Question

The existence of the unique solution of the system x +y +z=λ, 5 x-y+μ z=10, 2 x+3 y-z=6 depends on (A) μ only (B) λ only (C) λ and μ both (D) neither λ nor μ

Tardigrade Admin · Accepted Answer

For unique solution of the given system, Δ ≠ 0 i.e. |1 1 1 5 -1 μ 2 3 -1| ≠ 0 Hence, it depends only on μ.

Q. The existence of the unique solution of the system $x + y + z = λ, 5 x - y + μ z = 10, 2 x + 3 y - z = 6$ depends on

$μ$ only

$λ$ only

$λ$ and $μ$ both

neither $λ$ nor $μ$

For unique solution of the given system, $Δ \neq = 0$
i.e. $∣ ∣ 152 1 - 1 3 1 μ - 1 ∣ ∣ \neq = 0$
Hence, it depends only on $μ$ .

Q. The existence of the unique solution of the system x+y+z=λ,5x−y+μz=10,2x+3y−z=6 depends on

μ only

λ only

λ and μ both

neither λ nor μ