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KCET2019MathematicsMatrices

The inverse of the matrix ( [ array rrr 2 & 5 & 0 0 & 1 & 1 -1 & 0 & 3 array ] ) is

Options

  1. A( [ array ccc 3 & -5 & 5 -1 & -6 & -2 1 & -5 & 2 array ] )
  2. B( [ array ccc 3 & -15 & 5 -1 & 6 & -2 1 & -5 & -2 array ] )
  3. C( [ array ccc 3 & -1 & 1 -15 & 6 & -5 5 & -2 & 2 array ] )
  4. D( [ array ccc 3 & -15 & 5 -1 & 6 & -2 1 & -5 & 2 array ] )

Correct answer

D. ( [ array ccc 3 & -15 & 5 -1 & 6 & -2 1 & -5 & 2 array ] )

Step-by-step solution

(D) [ array l Let A= [ array ccc 2 & 5 & 0 0 & 1 & 1 -1 & 0 & 3 array ] |A|=2(3-0)-5(0+1) =6-5=1 |A|=1 array ] [ array l adj A= [ array ccc 3 & -1 & 1 -15 & 6 & -5 5 & -2 & 2 array ]^ T = [ array ccc 3 & -15 & 5 -1 & 6 & -2 1 & -5 & 2 array ] A⁻¹= a d j A |A| = [ array ccc 3 & -15 & 5 -1 & 6 & -2 1 & -5 & 2 array ] array ]

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