Question

If |(a₁, b₁, c₁), (a₂, b₂, c₂), (a₃, b₃, c₃)| ≠ 0, then the number of solutions of the system of equations a₁x + b₁y + c₁z = 0, a₂x + b₂y + c₂z = 0 and a₃x + b₃y + c₃z = 0 is

(A) Infinite number of solutions

(B) Only one unique solution

(C) More than one solution

(D) None of these

Answer 1

Answer is (B) Only one unique solution

If A ≠ 0 , then homogeneous system of linear equations AX = 0 has only trivial solution, i.e. X = 0.