Question

In a system of three linear non-homogeneous equations with three unknowns, if $\Delta =0$, and ${\Delta }_x=0,{\Delta }_y\ne 0,{\Delta }_z=0$, then the system has

• A. Unique solution
• B. Two solutions
• C. Infinitely many solutions
• D. No solution

Answer 1

Answer: (D)

No solution

Facts:

(1) If all $\Delta ,{\Delta }_x,{\Delta }_y,{\Delta }_z$ are zero then there will be infinite number of solution

(2) If $\Delta =0$ and any of ${\Delta }_x,{\Delta }_y,{\Delta }_z$ is non-zero then there will be no solution

and

(1) If $\Delta \ne 0$ then there will be an unique solution