The value of $\left| \begin{matrix} 1 & 1 & 1 \ \left( 2^{x} + 2^{- x} ight)^{2} & \left( 3^{x} + 3^{- x} ight)^{2} & \left( 5^{x} + 5^{- x} ight)^{2} \ \left( 2^{x} - 2^{- x} ight)^{2} & \left( 3^{x} - 3^{- x} ight)^{2} & \left( 5^{x} - 5^{- x} ight)^{2} \end{matrix} ight|$ is

Question

The value of $\left| \begin{matrix} 1 & 1 & 1 \ \left( 2^{x} + 2^{- x} ight)^{2} & \left( 3^{x} + 3^{- x} ight)^{2} & \left( 5^{x} + 5^{- x} ight)^{2} \ \left( 2^{x} - 2^{- x} ight)^{2} & \left( 3^{x} - 3^{- x} ight)^{2} & \left( 5^{x} - 5^{- x} ight)^{2} \end{matrix} ight|$ is

Dr. Abubacker · Accepted Answer

(a)
Applying $R_{2} ightarrow R_{2} - R_{3},\$we get
$\left| \begin{matrix}
1 & 1 & 1 \
4 & 4 & 4 \
\left( 2^{x} - 2^{- x} ight)^{2} & \left( 3^{x} - 3^{- x} ight)^{2} & \left( 5^{x} - 5^{- x} ight)^{2}
\end{matrix} ight|$
$= 4\left| \begin{matrix}
1 & 1 & 1 \
1 & 1 & 1 \
\left( 2^{x} - 2^{- x} ight)^{2} & \left( 3^{x} - 3^{- x} ight)^{2} & \left( 5^{x} - 5^{- x} ight)^{2}
\end{matrix} ight|$
$= 4 	imes 0 = 0\ \ \ \ \ \ \ \ \ \ \ \lbrack	herefore two\ rows\ are\ identicalbrack$

Q. The value of $\left| \begin{matrix} 1 & 1 & 1 \\ \left( 2^{x} + 2^{- x} \right)^{2} & \left( 3^{x} + 3^{- x} \right)^{2} & \left( 5^{x} + 5^{- x} \right)^{2} \\ \left( 2^{x} - 2^{- x} \right)^{2} & \left( 3^{x} - 3^{- x} \right)^{2} & \left( 5^{x} - 5^{- x} \right)^{2} \end{matrix} \right|$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?