Let P = 2 α 5 - 3 α 2 and Q = 2 l - m 5 n are two matrices, where l , m , n , α ∈ R , then the value of determinant P Q is equal to

Question

Let P = 2 α 5 - 3 α 2 and Q = 2 l - m 5 n are two matrices, where l , m , n , α ∈ R , then the value of determinant P Q is equal to, 0, - 1, 2, not possible

MARKS App · Accepted Answer

P Q = 4 l α - 2 m α 10 n α 10 l - 5 m 25 n - 6 l α 2 3 m α 2 - 15 n α 2 P Q = 4 l α - 2 m α 10 n α 10 l - 5 m 25 n - 6 l α 2 3 m α 2 - 15 n α 2 = 2 l m 5 n 2 α - 2 α 2 α 5 - 5 5 - 3 α 2 3 α 2 - 3 α 2 Here, C 1 and C 3 are identical ⇒ P Q = 0

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