Adnan
Code: Select all
\left[
\begin{array}{c | c}
A & B \\ \hline
C & D
\end{array}
\right]^{-1}
Code: Select all
\begin{align*}
& \left[
\displaystyle \begin{array}{c c c c c c c c c c c}
\frac{1-q_2^}{q_2^n} & \frac{1-q_2}{q_2^{n-1}} & \frac{1-q_2}{q_2^{n-2}} &\cdots & \frac{1-q_2}{q_2} & \frac{1}{q_2} & 1 & 0 & \cdots &0
\end{array}\right] \times
\left[
\begin{array}{c}
1 \\
\vdots \\
\vdots \\
\vdots \\
1 \\
\end{array}\right] \\
& = \frac{(1-q_2)+(q_2-q_2^2)+(q_2^2-q_2^3)+ \cdots +(q_2^{n-2}-q_2^{n-1})+(q_2^{n-1})+q_2^n+0+ \cdots +0}{q_2^n} \\
& = \frac{1 + q_2^n}{q_2^n}
\end{align*}