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The equations $λx – y =2, 2x – 3y = –λ, 3x – 2y = –1$ are consistent for |
$λ= –4$ $λ = –1, 4$ $λ= –1$ $λ = 1, –4$ |
$λ = –1, 4$ |
$\begin{vmatrix}λ&-1&-2\\2&-3&λ\\3&-2&1\end{vmatrix}=0$ $⇒λ(–3 + 2λ) + 1 (2 – 3λ) – 2(–4 + 9) + 0$ $⇒ 2λ^2 – 6λ – 8 = 0 ⇒ λ^2 – 3λ – 4 = 0$ $⇒(λ – 4) (λ + 1) = 0$ $∴ λ = –1, 4$ |
