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] 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]](https://tex.z-dn.net/?f=++A%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B2%5C%5C3%26amp%3B4%5C%5C%5Cend%7Barray%7D%5Cright%5D++B%3D+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B0%26amp%3B2%5C%5C0%26amp%3B3%26amp%3B4%5C%5C5%26amp%3B6%26amp%3B0%5Cend%7Barray%7D%5Cright%5D+)
Soluções para a tarefa
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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]
\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]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B2%5C%5C3%26amp%3B4%5C%5C%5Cend%7Barray%7D%5Cright%5D.+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B2%5C%5C3%26amp%3B4%5C%5C%5Cend%7Barray%7D%5Cright%5D+++%3D+%5C%5C%5C%5C%0A+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1.1+%2B+2.3%26amp%3B1.2+%2B+2.4%5C%5C3.1+%2B+4.3%26amp%3B3.2+%2B+4.4%5C%5C%5Cend%7Barray%7D%5Cright%5D+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%26amp%3B10%5C%5C15%26amp%3B22%5C%5C%5Cend%7Barray%7D%5Cright%5D+%0A+%0A)
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] \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]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B0%26amp%3B2%5C%5C0%26amp%3B3%26amp%3B4%5C%5C5%26amp%3B6%26amp%3B0%5Cend%7Barray%7D%5Cright%5D.%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B0%26amp%3B2%5C%5C0%26amp%3B3%26amp%3B4%5C%5C5%26amp%3B6%26amp%3B0%5Cend%7Barray%7D%5Cright%5D+%3D+%5C%5C%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1.1+%2B+0.0+%2B+2.5+%26amp%3B1.0+%2B+0.3+%2B+2.6%26amp%3B1.2%2B+0.4+%2B2.0%5C%5C+0.1+%2B+3.0+%2B+4.5%26amp%3B+0.0+%2B+3.3+%2B+4.6+%26amp%3B0.2+%2B+3.4+%2B+4.0%5C%5C5.1+%2B+6.0+%2B+0.5%26amp%3B+5.0+%2B+6.3+%2B+0.6%26amp%3B5.2+%2B+6.4+%2B+0.0%5Cend%7Barray%7D%5Cright%5D+%3D+%5C%5C%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D11%26amp%3B12%26amp%3B2%5C%5C20%26amp%3B33%26amp%3B12%5C%5C5%26amp%3B18%26amp%3B34%5Cend%7Barray%7D%5Cright%5D)
A² =
B² =
taissatg:
na segunda coluna da matriz A.. meus resultados deram 15 e 22.. os seus deram 12 e 19... conserta isso kkkk
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matriz ao quadrado se faz assim
ex:
a= 1 2 --> 1.1 2.2 --> 1 4
3 4 3.3 4.4 9 16
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