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Question Number 84068 by Power last updated on 09/Mar/20

Commented by Power last updated on 09/Mar/20

$prove it please$
Commented by Power last updated on 09/Mar/20

$please see$
Commented by TANMAY PANACEA last updated on 09/Mar/20

Commented by arcana last updated on 20/Mar/20

$para el caso n = 4$ $\| \begin{matrix} 1 + a_{1} & 1 & 1 & 1 \\ 1 & 1 + a_{2} & 1 & 1 \\ 1 & 1 & 1 + a_{3} & 1 \\ 1 & 1 & 1 & 1 + a_{4} \end{matrix} \| = \| \begin{matrix} a_{1} & 0 & 0 & - a_{4} \\ 0 & a_{2} & 0 & - a_{4} \\ 0 & 0 & a_{3} & - a_{4} \\ 1 & 1 & 1 & 1 + a_{4} \end{matrix} \|$ $= - \| \begin{matrix} 0 & 0 & - a_{4} \\ a_{2} & 0 & - a_{4} \\ 0 & a_{3} & - a_{4} \end{matrix} \| + \| \begin{matrix} a_{1} & 0 & - a_{4} \\ 0 & 0 & - a_{4} \\ 0 & a_{3} & - a_{4} \end{matrix} \| - \| \begin{matrix} a_{1} & 0 & - a_{4} \\ 0 & a_{2} & - a_{4} \\ 0 & 0 & - a_{4} \end{matrix} \| + a_{1} a_{2} a_{3} (1 + a_{4})$ $= a_{2} a_{3} a_{4} + a_{1} a_{3} a_{4} + a_{1} a_{2} a_{4} + a_{1} a_{2} a_{3} + a_{1} a_{2} a_{3} a_{4}$ $= a_{1} a_{2} a_{3} a_{4} (1 + \frac{1}{a_{1}} + \frac{1}{a_{2}} + \frac{1}{a_{3}} + \frac{1}{a_{4}})$ $para el caso general puede usarse induccion$ $matematica$ $A l g e b r a l i n e a r - Friedberg$
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