Question

Sendo A=  $\left[\begin{array}{ccc}5&2\\3&4\end{array}\right]$  e B= $\left[\begin{array}{ccc}1&1\\2&5\end{array}\right]$
                
a) Calcule AB
b) Calcule BA
c) Calcule A²
d) Calcule B²

Answer 1

Olá
 
a)Calculando AB, temos.

$AB= \left[\begin{array}{ccc}5.1+2.2&3.1+2.5&\\3.1+4.2&3.1+4.5\\\end{array}\right] = \left[\begin{array}{ccc}9&13\\11&23\\\end{array}\right]$

⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔
b) Calundado  BA, temos.

$BA= \left[\begin{array}{ccc}1.5+1.3&1.2+1.4\\2.5+5.3&2.2+5.4\\\end{array}\right] = \left[\begin{array}{ccc}8&6\\25&24\\\end{array}\right]$

⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔
c) Calulando  A², temos.

$A^{2} = \left[\begin{array}{ccc}5.5+2.3&5.2+2.4\\3.5+4.3&3.2+4.4\\\end{array}\right] = \left[\begin{array}{ccc}31&18\\27&22\\\end{array}\right]$

⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔⇔
d) calculando B², temos.

$B^{2} = \left[\begin{array}{ccc}1.1+1.2&1.1+1.5\\2.1+5.1&2.1+5.5\\\end{array}\right]= \left[\begin{array}{ccc}3&6\\12&27\\\end{array}\right]$

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                                         Espero ter ajudado!!