Question

If the matrix Mr is given by Mr=$\begin{pmatrix}r &r-1 \\\ r-1&r \end{pmatrix}$ for r=1,2,3....then det(M1)+det(M2)+.......+det(M2008)=

• A. 2007
• B. 2008
• C. (2008)2
• D. (2007)2

Answer 1

Answer: (C)

(2008)2

Answer 2

The correct answer is option (C): (2008)2

$det(M_r)=\begin{vmatrix} r &r-1 \\\ r-1&r \end{vmatrix}=2r-1$

$\sum_{r=1}^{2008} det(M_r)=2\sum_{r=1}^{2008}(r-2008)$

$=2\times\frac{2008\times2009}{2}-2008$

$=(2008)^2$