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KCET2009MathematicsMatrices

If A= [ array lll 2 & 1 & 0 0 & 2 & 1 1 & 0 & 2 array ] , then | adj A| is equal to

Options

  1. A0
  2. B9
  3. C1 9
  4. D81

Correct answer

D. 81

Step-by-step solution

Given, A= [ array lll 2 & 1 & 0 0 & 2 & 1 1 & 0 & 2 array ] C ₁₁=4, C ₁₂=1, C ₁₃=-2C₂₁=-2, C₂₂=4, C₂₃=1 C ₃₁=1, C ₃₂=-2, C ₃₃=4 adj (A)= [ array rrr 4 & 1 & -2 -2 & 4 & 1 1 & -2 & 4 array ]^ T = [ array rrr 4 & -2 & 1 1 & 4 & -2 -2 & 1 & 4 array ] | adj A |=4(16+2)+2(4-4)+(1+8)=72+0+9=81

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