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NDA2025MathematicsDeterminantsActual

The value of the determinant vmatrix a & b & c l & m & n p & q & r vmatrix is equal to

Options

  1. Avmatrix a & b & c p & q & r l & m & n vmatrix
  2. Bvmatrix l & m & n a & b & c p & q & r vmatrix
  3. Cvmatrix p & q & r a & b & c l & m & n vmatrix
  4. Dvmatrix a & p & l b & q & m c & r & n vmatrix

Correct answer

C. vmatrix p & q & r a & b & c l & m & n vmatrix

Step-by-step solution

Let = vmatrix a & b & c l & m & n p & q & r vmatrix Interchanging the first and third rows ( R₁ R₃ ), the sign of the determinant changes: = - vmatrix p & q & r l & m & n a & b & c vmatrix Now, interchanging the second and third rows ( R₂ R₃ ), the sign changes again: = - ( - vmatrix p & q & r a & b & c l & m & n vmatrix ) = vmatrix p & q & r a & b & c l & m & n vmatrix Answer: vmatrix p & q & r a & b & c l & m & n vmatrix

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