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For the system lambda*x + y + z = 1, x + lambda*y + z = lambda, x + y + lambda*z = lambda², match Column-I with the nature of solution in Column-II. Column-I: (A) lambda = 1, (B) general lambda not 1 and not -2, (C) lambda not 1 and not -2, (D) lambda = -2 Column-II: (P) unique solution, (Q) infinite solutions, (R) no solution, (S) finitely many solutions

1. A-Q, C-P, D-R
2. A-P, C-Q, D-R
3. A-R, C-P, D-Q
4. A-Q, C-R, D-P

Correct answer: A-Q, C-P, D-R

Solution

Determinant = (lambda-1)²(lambda+2): for lambda not 1 and not -2 unique; at lambda = 1 the equations coincide giving infinite solutions; at lambda = -2 the system is inconsistent (no solution).

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