Question

Select the correct option from the given alternatives:

The system 3x – y + 4z = 3, x + 2y – 3z = –2 and 6x + 5y + λz = –3 has at least one Solution when

Options

• λ = –5

• λ = 5

• λ = 3

• λ = –13

Answer 1

λ = –5

Explanation:

The given system of equations will have more than one solution if

`|(3, -1, 4),(1, 2, -3),(6, 5, lamda)|` = 0

Applying R₃ → R₃ – (R₁ + 3R₂), we get

`|(3, -1, 4),(1, 2, -3),(0, 0, lambda + 5)|` = 0

∴ 3[2(λ + 5) – 0] – (–1) (λ + 5 – 0) + 4(0 – 0) = 0

∴ 7λ + 35 = 0

∴ λ = `-35/7`

= – 5