question_answer

Matrix \[{{M}_{r}}\] is defined as  \[{{M}_{r}}=\left[ \begin{matrix}    r & r-1  \\    r-1 & r  \\ \end{matrix} \right],\,\,\,r\in N.\] If value of \[\det \left( {{M}_{1}} \right)+\det \,\left( {{M}_{2}} \right)+\det \,\left( {{M}_{3}} \right)+.....\] \[+\det \left( {{M}_{2007}} \right)is\,k\left( 2007 \right)\] then find k.

Answer:

2007.00