Math, asked by raomannu, 11 months ago

A=(1/0 1/1) where nEN then A* is​

Answers

Answered by MaheswariS
2

Answer:

\bf\,A^n=\left(\begin{array}{cc}1&0\\n&1\end{array}\right)

Step-by-step explanation:

\text{Given: }

\boxed{\bf\,A=\left(\begin{array}{cc}1&0\\1 &1\end{array}\right)}

A^2=\left(\begin{array}{cc}1&0\\1 &1\end{array}\right)\times\left(\begin{array}{cc}1&0\\1 &1\end{array}\right)

\implies\,A^2=\left(\begin{array}{cc}1+0&0+0\\1+1&0+1\end{array}\right)

\implies\,\boxed{\bf\,A^2=\left(\begin{array}{cc}1&0\\2&1\end{array}\right)}

\text{similarly,}

\boxed{\bf\,A^3=\left(\begin{array}{cc}1&0\\3&1\end{array}\right)}

\boxed{\bf\,A^4=\left(\begin{array}{cc}1&0\\4&1\end{array}\right)}

and so on

\text{Hence }

\boxed{\bf\,A^n=\left(\begin{array}{cc}1&0\\n&1\end{array}\right)}

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