Let $α λ, μ \in R$ consider the system of linear equations $α x + 2 y = λ, 3 x - 2 y = μ$ which of the following statement(s) is correct?

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If $λ = μ \neq 0$ then system has no solution for $α = - 3$

If $λ + μ = 0$ then the system has infinitely many solutions for $α = - 3$

If $α = - 3$ then the system has infinitely many solutions for all values of $λ a n d μ$

If $α \neq - 3$ then the system has a unique solution for all values of $λ a n d μ$

answer is B, C.

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Detailed Solution

Condition: $|\begin{matrix} α & 2 \\ 3 & - 2 \end{matrix}| = 0; - 2 α - 6 = 0$

$|\begin{matrix} λ & 2 \\ μ & - 2 \end{matrix}| = 0; - 2 λ - 2 μ = 0$

$λ + μ = 0$

Det A = O for infinitely many solutions

$\det A \neq 0$ for unique solution

$∴ α \neq - 3$

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