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AP EAMCET202125 Aug 2021Morning ShiftMathematicsDeterminantsActual

The values of x for which the given matrix [ array ccc -x & x & 2 2 & x & -x x & -2 & -2 array ] will be non-singular are

Options

  1. A-2 x 2
  2. Bfor all x other than 2 and -2
  3. Cx 2
  4. Dx -2

Correct answer

B. for all x other than 2 and -2

Step-by-step solution

Let A= [ array ccc -x & x & 2 2 & x & -x x & -2 & -2 array ]A is non-singular matrix, aligned & |A| 0 & |A|=-x(-2 x-2 x)-x (-4+x^2 )+2 (-4-x^2 ) 0 & 4 x^2+4 x-x^3-8-2 x^2 0 & x^3-2 x^2-4 x+8 0 & (x-2)^2(x+2) 0 & x -2,2 aligned

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