Determinants Matrices Question 37
Question: Matrix $ M _{r} $ is defined as $ M _{r}=( \begin{matrix} r & r-1 \\ r-1 & r \\ \end{matrix} ), $
$ r\in N $ . The value of $ det(M_1)+\det (M_2)+\det (M_3)+….+\det (M _{2014}) $ is
Options:
A) $ 2013 $
B) $ 2014 $
C) $ {{(2013)}^{2}} $
D) $ {{(2014)}^{2}} $
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] det $ (Mr)= \begin{vmatrix} r & r-1 \\ r-1 & r \\ \end{vmatrix}=2r-1 $
$ \sum\limits _{r=1}^{2014}{\det (M _{r})=2\sum\limits _{r=1}^{2014}{r-2014}} $
$ =2\times \frac{2014\times 2015}{2}-2014={{(2014)}^{2}} $
BETA
