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MHT CET202521 Apr 2025Morning ShiftMathematicsMatricesActual

The third element in the second row of adjoint of a matrix A = [ a _ ij ]_ 3 3 ( . where . a _ ij =2 i + j ) is

Options

  1. A2
  2. B-2
  3. C4
  4. D-4

Correct answer

C. 4

Step-by-step solution

Adjoint element ( adj A )₂₃ corresponds to the cofactor C₃₂ of matrix A . Matrix A with elements a_ ij = 2i + j for i,j = 1,2,3 yields: A = bmatrix 3 & 4 & 5 5 & 6 & 7 7 & 8 & 9 bmatrix Cofactor C₃₂ = (-1)³⁺² M₃₂ = -M₃₂ , where M₃₂ is the determinant of the submatrix after removing row 3 and column 2: M₃₂ = bmatrix 3 & 5 5 & 7 bmatrix = 3 7 - 5 5 = 21 - 25 = -4 Thus, C₃₂ = -(-4) = 4 , and ( adj A )₂₃ = 4 . The final answer is C

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