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Black Book Advanced Problems in MathematicsMathematicsDeterminants

Let ₁ = vmatrix a₁ & a₂ & a₃ b₁ & b₂ & b₃ c₁ & c₂ & c₃ vmatrix ₂ = vmatrix 6a₁ & 2a₂ & 2a₃ 3b₁ & b₂ & b₃ 12c₁ & 4c₂ & 4c₃ vmatrix and ₃ = vmatrix 3a₁+b₁ & 3a₂+b₂ & 3a₃+b₃ 3b₁ & 3b₂ & 3b₃ 3c₁ & 3c₂ & 3c₃ vmatrix then ₃ - ₂ = k ₁, find k.

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3

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