If A_ = ( * 20 c & - 1 - 1 & ); , N then |A_1| + |A_2| + ..... + … - Vidyadip

MCQ

If ${A_\lambda } = \left( {\begin{array}{*{20}{c}}
\lambda &{\lambda - 1}\\
{\lambda - 1}&\lambda
\end{array}} \right);\,\lambda \in N$ then $|A_1| + |A_2| + ..... + |A_{300}|$ is equal to

A
$(299)^2$
✓
$(300)^2$
C
$(301)^2$
D
None of these

✓

Answer

Correct option: B.

$(300)^2$

b
$\sum\limits_{\lambda = 1}^{\lambda = 300} {\left| A \right|\sum\limits_{\lambda = 1}^{\lambda = 300} {\left[ {{\lambda ^2} - {{\left( {\lambda - 1} \right)}^2}} \right]} = {{\left( {300} \right)}^2}} $

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