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If the matrix Mr is given by Mr = open square brackets table row r cell r minus 1 end cell row cell r minus 1 end cell r end table close square brackets, r = 1, 2, 3 .... Then the value of det (M1) + det(M2) + .... + det (M2009) is

  1. 2008    
  2. 2009    
  3. (2009)2    
  4. (2008)2    

The correct answer is: (2009)2


    Mr = open square brackets table row r cell r minus 1 end cell row cell r minus 1 end cell r end table close square brackets
    |Mr| = r2 – (r – 1)2 = 2r – 1
    rightwards double arrow sum subscript r equals 1 end subscript superscript n vertical line M subscript r vertical line = not stretchy sum subscript r equals 1 end subscript superscript n end superscript left parenthesis 2 r minus 1 right parenthesis = n2

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