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NDA2020MathematicsDeterminantsActual

For how many values of k , is the matrix [ array ccc 0 & k & 4 -k & 0 & -5 -k & k & -1 array ] singular?

Options

  1. AOnly one
  2. BOnly two
  3. COnly four
  4. DInfinite

Correct answer

D. Infinite

Step-by-step solution

For singular matrix, [ array ccc 0 & K & 4 -K & 0 & -5 -K & K & -1 array ]=0 aligned & K(5 K-K)+4 (-K^2 )=0 & 4 K^2-4 K^2=0 aligned Hence, for all values of K , the given matrix is singular matrix.

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