Question

$A=\left[ \begin{matrix} 1& k^{2}\\ 0& 1\end{matrix} \right]$ ve $A^{k}=\left[ \begin{matrix} 1& 64\\ 0& 1\end{matrix} \right]$ old. gore k kactir?

Answer 1

$$\left[\begin{matrix}1 & a\\0 &1\end{matrix}\right]\cdot\left[\begin{matrix}1 & b\\0 &1\end{matrix}\right]=\left[\begin{matrix}1 & a+b\\0 &1\end{matrix}\right]$$ oldugundan $$A^k=\left[\begin{matrix}1 & \underbrace{k^2+k^2+\cdots+k^2}_{k \text{ tane}}\\0 &1 \end{matrix}\right]=\left[\begin{matrix}1 & k^3\\0 &1\end{matrix}\right]$$ olur.

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