Question

5) A = [[2, 3], [3, 4]] encontre o valor de A ^ 2 - 4A​

Answer 1

Resposta

A² - 4a =

Vamos calcular separado

Calculando A²

$A^2=A\times A\\ \\A^2= \left[\begin{array}{ccc}2&3\\3&4\end{array}\right] X\left[\begin{array}{ccc}2&3\\3&4\end{array}\right] \\ \\ \\ A^2=\left[\begin{array}{ccc}2.2+3.3&2.3+3.4\\3.2+4.3&3.3+4.4\end{array}\right] =\left[\begin{array}{ccc}4+9&6+12\\6+12&9+16\end{array}\right]$

$A^2=\left[\begin{array}{ccc}13&18\\18&25\end{array}\right]$

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Calculando 4A

$4\left[\begin{array}{ccc}2&3\\ 3&4\end{array}\right] =\left[\begin{array}{ccc}4.2&4.3\\ 4.3&4.4\end{array}\right] =\left[\begin{array}{ccc}8&12\\12&16\end{array}\right]$

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Calculando A²-4A

$A^2-4A=\left[\begin{array}{ccc}13&18\\18&25\end{array}\right] -\left[\begin{array}{ccc}8&12\\12&16\end{array}\right] \\ \\ \\ A^2-4A=\left[\begin{array}{ccc}13-8&18-12\\18-12&25-16\end{array}\right] \\ \\ \\ A^2-4A=\left[\begin{array}{ccc}5&6\\6&9\end{array}\right]$