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KCET2014MathematicsSets and Relations

The inverse of the matrix ( A= [ array lll 2 & 0 & 0 0 & 3 & 0 0 & 0 & 4 array ] ) is

Options

  1. A( [ array lll 2 & 0 & 0 0 & 3 & 0 0 & 0 & 4 array ] )
  2. B( 1 24 [ array lll 1 / a & 0 & 0 0 & 1 / b & 0 0 & 0 & 1 / c array ] )
  3. C( 1 24 [ array lll 2 & 0 & 0 0 & 3 & 0 0 & 0 & 4 array ] )
  4. D( 1 24 [ array llll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] )

Correct answer

B. ( 1 24 [ array lll 1 / a & 0 & 0 0 & 1 / b & 0 0 & 0 & 1 / c array ] )

Step-by-step solution

Given that ( A= [ array lll 2 & 0 & 0 0 & 3 & 0 0 & 0 & 4 array ] ) Now ( A⁻¹= [ array ccc 1 / 2 & 0 & 0 0 & 1 / 3 & 0 0 & 0 & 1 / 4 array ] ) If ( A= [ array ccc a & 0 & 0 0 & b & 0 0 & 0 & c array ] ), then ( A⁻¹= [ array ccc 1 / a & 0 & 0 0 & 1 / b & 0 0 & 0 & 1 / c array ] ) When ( a 0, b 0, c 0 )

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