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MHT CET2009MathematicsMatrices

If A= [ array lll 3 & 2 & 4 1 & 2 & 1 3 & 2 & 6 array ] and A_ i j are the cofactors of a_ y , then a₁₁ A₁₁+a₁₂ A₁₂+a₁₃ A₁₃ is equal to

Options

  1. A8
  2. B6
  3. C4
  4. D0

Correct answer

A. 8

Step-by-step solution

aligned a₁₁ A₁₁+a₁₂ A₁₂ &+a₁₃ A₁₃ &=3 | array ll 2 & 1 2 & 6 array |-2 | array ll 1 & 1 3 & 6 array |+4 | array ll 1 & 2 3 & 2 array | &=3(12-2)-2(6-3)+4(2-6) &=30-6-16 &=8 aligned

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