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Maths-

General

Easy

Question

Matrix M_r is defined as M_r= $open square brackets table row r cell r – 1 end cell row cell r – 1 end cell r end table close square brackets$ , r $element of$ N. Then det. (M₁) + det.(M₂) + ........... + det.(M₂₀₀₉) = ?

2009
(2009)²
(2009)³
None of these

The correct answer is: (2009)²

det.(M_r) = r² – (r –1)² = 2r –1
$not stretchy sum subscript r equals 1 end subscript superscript 2009 end superscript left parenthesis 2 r – 1 right parenthesis$ = 2 × $open parentheses fraction numerator 2009 cross times 2010 over denominator 2 end fraction close parentheses$ – 2009
= (2009) × (2009) = (2009)²

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