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AP EAMCET20227 Jul 2022Morning ShiftMathematicsMatricesActual

If A= [ array lll x & 2 & 1 2 & x & 1 2 & 1 & 0 array ] and det (A^3 )=125 , then x=

Options

  1. A1 / 3
  2. B3
  3. C- 1 3
  4. D-3

Correct answer

A. 1 / 3

Step-by-step solution

|A|= | array lll x & 2 & 1 2 & x & 1 2 & 1 & 0 array |=x(0-1)-2(0-2)+1(2-2 x)=6-3 x According to question, |A^3 |=125 |A|^3=5^3 [ |A^3 |=|A|^3 ] aligned & & |A| & =5 & & 6-3 x & =5 & & x & =1 / 3 aligned

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