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NDA2013MathematicsDeterminantsActual

The value of the determinant | array ccc m & n & p p & m & n n & p & m array |

Options

  1. Ais a perfect cube
  2. Bis a perfect square
  3. Chas linear factor
  4. Dis zero

Correct answer

C. has linear factor

Step-by-step solution

(m+n+p) | array ccc 1 & n & p 1 & m & n 1 & p & m array |(m+n+p) | array ccc 1 & n & p 0 & m-n & n-p 0 & p-n & m-p array | aligned & =(m+n+p) (m^2-m p-m n+n p-n p+p^2+n^2-n p ) & =(m+n+p) (m^2+n^2+p^2-m n-n p-p m ) aligned

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