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NDA2021MathematicsDeterminantsActual

With the numbers 2,4,6,8 , all the possible determinants with these four different elements are constructed. What is the sum of the values of all such determinants?

Options

  1. A128
  2. B64
  3. C32
  4. D0

Correct answer

D. 0

Step-by-step solution

All possible determinants from 2,4,6 and 8 | array ll 8 & 6 4 & 2 array |+ | array ll 8 & 4 2 & 6 array |+ | array ll 2 & 4 8 & 6 array |+ | array ll 4 & 2 6 & 8 array |+ | array ll 4 & 8 6 & 2 array |+ | array ll 6 & 8 2 & 4 array | aligned &=(16-24)+(48-8)+(12-32)+(32-12) &+(8-48)+(24-16) &=0 aligned

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