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Investigate the values of $λ$ and $μ$ for the system $x + 2 y + 3 z = 6, x + 3 y + 5 z = 9, 2 x + 5 y + λ z = μ$ and match the values in List-I with items in List-II
List-I List-II
(A) $λ = 8, μ \neq 15$ (1) In finitely many solutions
(B) $λ \neq 8, μ \in R$ (2) No solution
(C) $λ = 8, μ = 15$ (3) Unique solution

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$\begin{matrix} A & B & C \\ 1 & 2 & 3 \end{matrix}$

$\begin{matrix} A & B & C \\ 2 & 3 & 1 \end{matrix}$

$\begin{matrix} A & B & C \\ 3 & 2 & 1 \end{matrix}$

$\begin{matrix} A & B & C \\ 3 & 1 & 2 \end{matrix}$

answer is B.

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Detailed Solution

$[A D] = [\begin{matrix} 1 & 2 & 3 & 6 \\ 1 & 3 & 5 & 9 \\ 2 & 5 & λ & μ \end{matrix}] \Rightarrow [\begin{matrix} 1 & 2 & 3 & 6 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & λ - 8 & μ - 15 \end{matrix}]$

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