Matrix A_ = [ * 20 c & - 1 - 1 & ], N then the value of | A_1 | +… - Vidyadip

MCQ

Matrix ${A_\lambda } = \left[ {\begin{array}{*{20}{c}}
\lambda &{\lambda - 1} \\
{\lambda - 1}&\lambda
\end{array}} \right],\lambda \in N$ then the value of $\left| {{A_1}} \right| + \left| {{A_2}} \right| + \left| {{A_3}} \right| + ....... + \left| {{A_{300}}} \right|$ is

A
$(299)^2$
✓
$(300)^2$
C
$(150)^2$
D
$(301)^2$

✓

Answer

Correct option: B.

$(300)^2$

b
$\left| {{{\rm{A}}_\lambda }} \right| = \left| {\begin{array}{*{20}{c}}
\lambda &{\lambda - 1}\\
{\lambda - 1}&\lambda
\end{array}} \right| = {\lambda ^2} - {[\lambda - 1)^2}$

$ = 2\lambda - 1$

$\therefore \left| {{{\rm{A}}_1}} \right| + \left| {{{\rm{A}}_2}} \right| + \left| {{{\rm{A}}_3}} \right| + \ldots . + \left| {{{\rm{A}}_{300}}} \right|$

$=1+3^{2}+5+\ldots . .+599 $

$= \frac{300}{2}(1+599)=(300)^{2} $

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