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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
Solution
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
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