Correct Option: C

Given equations are
x + 2y + z = 6
2x + y + 2z = 6
x + y + z = 5
Given system can be written as

Applying row operation
R₂ → R₂ – 2R₁, R₃ → R₃ – R₁

and applying R₃ → 3R₃ – R₁

Since the rank of co-efficient matrix is 2 and rank of argument matrix is 3, which is not equal. Hence system has no solution.