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NDA 1 2025 Maths, question 8

Topic: Matrices and determinants

Q8

If Δ=∣abcdefghi∣\Delta = \left| \begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix} \right| and A,B,C,D,GA,B,C,D,G are the cofactors of the elements a,b,c,d,ga,b,c,d,g respectively, then what is bB+cC−dD−gGbB + cC - dD - gG equal to?

  1. (a) 0Correct answer
  2. (b) 1
  3. (c) Δ\Delta
  4. (d) −Δ- \Delta

Solution.

Answer: (a) 0

  1. Expand the same determinant along its first row and first column: Δ=aA+bB+cC=aA+dD+gG\Delta = aA + bB + cC = aA + dD + gG.
  2. Subtracting the two expressions gives bB+cC−dD−gG=0bB + cC - dD - gG = 0.