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NDA2011MathematicsDeterminantsActual

What is the value of the determinant | array ccc x+1 & x+2 & x+4 x+3 & x+5 & x+8 x+7 & x+10 & x+14 array | ?

Options

  1. Ax+2
  2. Bx^2+2
  3. C2
  4. D-2

Correct answer

D. -2

Step-by-step solution

aligned & | array ccc x+1 & x+2 & x+4 x+3 & x+5 & x+5 x+7 & x+10 & x+14 array | & c₁ c₂-c₁, c₃-c₂ aligned | array ccc -1 & -2 & x+4 -2 & -3 & x+8 -3 & -4 & x+14 array | aligned & = | array ccc 1 & 2 & x+4 2 & 3 & x+8 3 & 4 & x+14 array | & = R ₂- R ₁, R ₃- R ₂ aligned aligned & | array ccc 1 & 2 & x+4 1 & 1 & 4 1 & 1 & 6 array | = & R ₁- R ₂, R ₂- R ₃ aligned aligned & | array ccc 0 & 1 & x 0 & 0 & -2 1 & 1 & 6 array | = & 1 (-2) =-2 . aligned

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