3 and 4 .Determinants and Matrices
normal

જો ${A_\lambda } = \left( {\begin{array}{*{20}{c}}
\lambda &{\lambda  - 1}\\
{\lambda  - 1}&\lambda 
\end{array}} \right);\,\lambda  \in N$ હોય તો  $|A_1| + |A_2| + ..... + |A_{300}|$ મેળવો.

A

$(299)^2$

B

$(300)^2$

C

$(301)^2$

D

એકપણ નહીં.

Solution

$\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}} $

Standard 12
Mathematics

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