Question
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?
NDA
Mathematics
Determinants
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 0
- B. 1
- C.
- D. -
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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