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If = vmatrix a & b & c d & e & f g & h & i vmatrix and A , B , C , D , G are the cofactors of the elements a , b , c , d , g respectively, then what is bB + cC - dD - gG equal to?

Options

  1. A0
  2. B1
  3. C-

Correct answer

A. 0

Step-by-step solution

The sum of the products of elements of any row or column with their corresponding cofactors is equal to the determinant . Expanding the determinant along the first row, we get: aA + bB + cC = Expanding the determinant along the first column, we get: aA + dD + gG = Subtracting the second equation from the first equation, we get: (aA + bB + cC) - (aA + dD + gG) = - bB + cC - dD - gG = 0 Answer: 0

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