If A - - - 2 0 0- 0 2 0- 0 0 2 - - then find A 5-

Given, A = [ [ 2 amp; 0 amp; 0; 0 amp; 2 amp; 0; 0 amp; 0 amp; 2 ]] #160; =2 [ [ 1 amp; 0 amp; 0; 0 amp; 1 am ...

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Multiplication of Matrices

If A = [ [ ...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 \end{matrix} ⎤ ⎥ ⎦,$ then find $A^{5}$ .

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Solution

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A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 \end{matrix} ⎤ ⎥ ⎦

A^{6} =

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 \end{matrix} ⎤ ⎥ ⎦

A^{- 1}

A = ⎡ ⎢ ⎣ \begin{matrix} 200 \end{matrix} \begin{matrix} 020 \end{matrix} \begin{matrix} 002 \end{matrix} ⎤ ⎥ ⎦

A^{5} =

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

A^{5} =

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

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