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KCET2009MathematicsDeterminants

If | array ccc 1+ ² & ² & 4 2 ² & 1+ ² & 4 2 ² & ² & 4 2 -1 array |=0 and 0 < < 2 , then 4 is equal to

Options

  1. A3 2
  2. B0
  3. C-1 2
  4. D1 2

Correct answer

D. 1 2

Step-by-step solution

Given, | array ccc 1+ ² & ² & 4 2 ² & 1+ ² & 4 2 ² & ² & 4 2 -1 array |=0 Applying C ₁ C ₁+ C ₂ | array ccc 2 & ² & 4 2 2 & 1+ ² & 4 2 1 & ² & 4 2 -1 array |=0 Applying R ₂ R ₂- R ₁, R ₃ 2 R ₃- R ₁ aligned & | array ccc 2 & ² & 4 2 0 & 1 & 0 0 & ² & 4 2 -2 array |=0 & 2(4 2 -2-0)=0 & 2 = 1 2 & Now, 4 =1-2 ² 2 &=1-2 ( 1 2 )²= 1 2 aligned

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