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KCET2007MathematicsMatrices

If A= [ array ccc 1 & -2 & 2 0 & 2 & -3 3 & -2 & 4 array ] , then A adj (A) is equal to

Options

  1. A[ array lll 5 & 1 & 1 1 & 5 & 1 1 & 1 & 5 array ]
  2. B[ array lll 5 & 0 & 0 0 & 5 & 0 0 & 0 & 5 array ]
  3. C[ array lll 8 & 0 & 0 0 & 8 & 0 0 & 0 & 8 array ]
  4. D[ array lll 0 & 0 & 0 0 & 0 & 0 0 & 0 & 0 array ]

Correct answer

C. [ array lll 8 & 0 & 0 0 & 8 & 0 0 & 0 & 8 array ]

Step-by-step solution

Given, A= [ array ccc 1 & -2 & 2 0 & 2 & -3 3 & -2 & 4 array ] aligned &C₁₁=8-6=2 &C₁₂=-(0+9)=-9, C₃₁=+6-4=2 &C₁₃=0-6=-6, C₃₂=-(-3-0)=3 &C₂₁=-(-8+4)=4, C₃₃=2-0=2 &C₂₂=4-6=-2, C₂₃=-(-2+6)=-4 aligned adj (A)= [ array ccc 2 & -9 & -6 4 & -2 & -4 2 & 3 & 2 array ]^ T = [ array ccc 2 & 4 & 2 -9 & -2 & 3 -6 & -4 & 2 array ] Now, A adj (A)= [ array ccc 1 & -2 & 2 0 & 2 & -3 3 & -2 & 4 array ] [ array ccc 2 & 4 & 2 -9 & -2 & 3 -6 & -4 & 2 array ] = [ array lll 8 & 0 & 0 0 & 8 & 0 0 & 0 & 8 array ] Alternative : A⁻¹= adj (A

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