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Question: If A<sub>r</sub> = \(\begin{pmatrix} r & r - 1 \\ r - 1 & r \end{pmatrix}\) where r is a natural num...

If Ar = (rr−1r−1r)\begin{pmatrix} r & r - 1 \\ r - 1 & r \end{pmatrix} where r is a natural number then

|A1| + |A2| + |A3| +……+ |A2006| must be equal to-

A

2006

B

(2006)2

C

(2006)3

D

2007

Answer

(2006)2

Explanation

Solution

|Ar| = r2 –(r –1)2 = 2r–1

Ž |A1| + |A2| + …..+ |A2006|

= ∑r=12006(2r−1)\sum_{r = 1}^{2006}{(2r - 1)}= ∑(2006)2\sum_{}^{}{(2006)^{2}}