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Paragraph: Let be the determinant of a matrix A , where A= ( array lll a₁₁ & a₁₂ & a₁₃ a₂₁ & a₂₂ & a₂₃ a₃₁ & a₃₂ & a₃₃ array ) and C₁₁, C₁₂, C₁₃ be the cofactors of a₁₁, a₁₂, a₁₃ respectively. Question: What is the value of | array lll a₂₁ & a₃₁ & a₁₁ a₂₃ & a₃₃ & a₁₃ a₂₂ & a₃₂ & a₁₂ array | ?

Options

  1. A0
  2. B1
  3. C-

Correct answer

3

Step-by-step solution

= | array lll a₁₁ & a₁₂ & a₁₃ a₂₁ & a₂₂ & a₂₃ a₃₁ & a₃₂ & a₃₃ array |= | array lll a₁₁ & a₂₁ & a₃₁ a₁₂ & a₂₂ & a₃₂ a₁₃ & a₂₃ & a₃₃ array | Apply C₁ C₃ Apply C₁ C₂=- | array lll a₃₁ & a₂₁ & a₁₁ a₃₂ & a₂₂ & a₁₂ a₃₃ & a₂₃ & a₁₃ array |=+ | array lll a₂₁ & a₃₁ & a₁₁ a₂₂ & a₃₂ & a₁₂ a₂₃ & a₃₃ & a₁₃ array | Apply R₂ R₃=- | array lll a₂₁ & a₃₁ & a₁₁ a₂₃ & a₃₃ & a₁₃ a₂₂ & a₃₂ & a₁₂ array |

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