• Aa unique solution of x=1, y=1 and z=1.
• Bonly the two solutions of (x=1, y=1, z=1) and (x=2, y=1, z=0).
• infinite number of solutions.
• Dno feasible solution.

The coefficient matrix has determinant 1(1−(−2))−2(2−2)+1(−2−1)=3−0−3=0, so the system is singular. Eq1 minus Eq3 gives 3y=3, so y=1; substituting y=1 into all three original equations reduces EACH of them to the same equation x+z=2 — meaning only 2 of the 3 equations are independent, leaving one free variable. This is a one-parameter family of solutions (a line), i.e. infinitely many — the two solutions listed in option (B), (1,1,1) and (2,1,0), both lie on this line but are not the only ones.