Question

Seja A uma Matiz quadrada de ordem n; definimos A²= A.A. Assim, determine A² nos seguintes casos:

a) A =


$A= \left[\begin{array}{ccc}1&2\\3&4\\\end{array}\right] B= \left[\begin{array}{ccc}1&0&2\\0&3&4\\5&6&0\end{array}\right]$

Answer 1

Bom, a regra de multiplicar matrizes é simples, tu vais pegar as linhas da primeira matriz e multiplicar com as colunas da segunda:
A² = 
$\left[\begin{array}{ccc}1&2\\3&4\\\end{array}\right]. \left[\begin{array}{ccc}1&2\\3&4\\\end{array}\right] = \\\\ \left[\begin{array}{ccc}1.1 + 2.3&1.2 + 2.4\\3.1 + 4.3&3.2 + 4.4\\\end{array}\right] = \left[\begin{array}{ccc}7&10\\15&22\\\end{array}\right]$
 
B² = 
$\left[\begin{array}{ccc}1&0&2\\0&3&4\\5&6&0\end{array}\right].\left[\begin{array}{ccc}1&0&2\\0&3&4\\5&6&0\end{array}\right] = \\\\ \left[\begin{array}{ccc}1.1 + 0.0 + 2.5 &1.0 + 0.3 + 2.6&1.2+ 0.4 +2.0\\ 0.1 + 3.0 + 4.5& 0.0 + 3.3 + 4.6 &0.2 + 3.4 + 4.0\\5.1 + 6.0 + 0.5& 5.0 + 6.3 + 0.6&5.2 + 6.4 + 0.0\end{array}\right] = \\\\ \left[\begin{array}{ccc}11&12&2\\20&33&12\\5&18&34\end{array}\right]$
 

Answer 2

matriz ao quadrado se faz assim

ex:

a= 1 2   -->  1.1  2.2  -->   1 4

    3 4        3.3 4.4         9 16