First slide

Introduction to Determinants

Question

If $A_{r} = (\begin{array}{cc} r & r - 1 \\ r - 1 & r \end{array})$ where r is a natural number then $\sqrt{[|A_{1}| + |A_{2}| + |A_{3}| + \dots . . . . . . . . + |A_{2008}|]}$ must be equal to

Moderate

A

2008
B

(2006)²
C

(2006)³
D

2007

Solution

$\begin{array}{r} |A_{r}| = r^{2} - (r - 1)^{2} = 2 r - 1 \\ \sqrt{\sum_{r = 1}^{2008} |A_{r}|} = \sqrt{(2008)^{2}} \end{array}$

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