If A = [ 1 1 0 1 ] , then A n =

Question

If $A = [\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}],$ then $A^{n} =$

Smart Achievers · Accepted Answer

(1)

Ans. $[\begin{matrix} 1 & n \\ 0 & 1 \end{matrix}]$

Explanation:

Let $A = [\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}]$

$A^{2} = A \times A$

$= [\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}]$

$= [\begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}]$

$A^{3} = A^{2} \times A$

$= [\begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}]$

$= [\begin{matrix} 1 & 3 \\ 0 & 1 \end{matrix}]$

$\begin{matrix} ⋮ & ⋮ & ⋮ \end{matrix}$

$A^{n} = [\begin{matrix} 1 & n \\ 0 & 1 \end{matrix}]$

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