Maths-
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Question

If D = diag [d1, d2, .....dn] is a diagonal matrix with di ≠ 0, i = 1, 2, 3,......, n, then D–1 is

  1. straight d subscript 1 superscript negative 1 end superscript d subscript 2 superscript negative 1 end superscript......d subscript n end subscript superscript negative 1 end superscriptIn    
  2. diag [d subscript n end subscript superscript negative 1 end superscript,d subscript n minus 1 end subscript superscript negative 1 end superscript, ....... d subscript 1 end subscript superscript negative 1 end superscript]    
  3. diag [straight d subscript 1 superscript negative 1 end superscriptd subscript 2 end subscript superscript negative 1 end superscript......d subscript n end subscript superscript negative 1 end superscript]    
  4. None of these    

The correct answer is: diag [straight d subscript 1 superscript negative 1 end superscriptd subscript 2 end subscript superscript negative 1 end superscript......d subscript n end subscript superscript negative 1 end superscript]


    Here |D| = d1d2d3 ........dn and
    adj D = [d2d3 ........dn, d1d3.........dn, ........ d1d2.......dn–1]
    rightwards double arrow D–1 = diag [d subscript 1 end subscript superscript negative 1 end superscript,d subscript 2 end subscript superscript negative 1 end superscript....... d subscript n end subscript superscript negative 1 end superscript]

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