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If the system of equations a₁ x+b₁ y+c₁ z=0 , a₂ x+b₂ y+c₂ z=0, a₃ x+b₃ y+c₃ z=0 has only trivial solution, then the rank of [ array lll a₁ & b₁ & c₁ a₂ & b₂ & c₂ a₃ & b₃ & c₃ array ] is

Options

  1. A2
  2. B1
  3. C3
  4. D0

Correct answer

C. 3

Step-by-step solution

If the system of equations a₁ x+b₁ y+c₁=0 , a₂ x+b₂ y+c₂ z=0 , and a₃ x+b₃ y+c₃=0 has only trivial solution, then rank of the matrix [ array lll a₁ & b₁ & c₁ a₂ & b₂ & c₂ a₃ & b₃ & c₃ array ] is 3 .

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