Matriz: Os elementos de uma matriz M quadrada de ordem 3x3 são dados por a i j, onde i+j, se i diferente j 0, se i=j. Determine M+M
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Bom dia!
Note que na diagonal principal os valores serão zero:
![\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right] \ \rightarrow \ M= \left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_%7B11%7D%26amp%3Ba_%7B12%7D%26amp%3Ba_%7B13%7D%5C%5Ca_%7B21%7D%26amp%3Ba_%7B22%7D%26amp%3Ba_%7B23%7D%5C%5Ca_%7B31%7D%26amp%3Ba_%7B32%7D%26amp%3Ba_%7B33%7D%5Cend%7Barray%7D%5Cright%5D+%5C+%5Crightarrow+%5C+M%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26amp%3B3%26amp%3B4%5C%5C3%26amp%3B0%26amp%3B5%5C%5C4%26amp%3B5%26amp%3B0%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right] \ \rightarrow \ M= \left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right]")
M + M:
![M+M= \left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right] + \left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right] = \left[\begin{array}{ccc}0+0&3+3&4+4\\3+3&0+0&5+5\\4+4&5+5&0+0\end{array}\right] \\ M+M= \left[\begin{array}{ccc}0&6&8\\6&0&10\\8&10&0\end{array}\right]](https://tex.z-dn.net/?f=M%2BM%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26amp%3B3%26amp%3B4%5C%5C3%26amp%3B0%26amp%3B5%5C%5C4%26amp%3B5%26amp%3B0%5Cend%7Barray%7D%5Cright%5D+%2B++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26amp%3B3%26amp%3B4%5C%5C3%26amp%3B0%26amp%3B5%5C%5C4%26amp%3B5%26amp%3B0%5Cend%7Barray%7D%5Cright%5D+%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%2B0%26amp%3B3%2B3%26amp%3B4%2B4%5C%5C3%2B3%26amp%3B0%2B0%26amp%3B5%2B5%5C%5C4%2B4%26amp%3B5%2B5%26amp%3B0%2B0%5Cend%7Barray%7D%5Cright%5D+%5C%5C+M%2BM%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26amp%3B6%26amp%3B8%5C%5C6%26amp%3B0%26amp%3B10%5C%5C8%26amp%3B10%26amp%3B0%5Cend%7Barray%7D%5Cright%5D+ "M+M= \left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right] + \left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right] = \left[\begin{array}{ccc}0+0&3+3&4+4\\3+3&0+0&5+5\\4+4&5+5&0+0\end{array}\right] \\ M+M= \left[\begin{array}{ccc}0&6&8\\6&0&10\\8&10&0\end{array}\right]")
Note que na diagonal principal os valores serão zero:
M + M:
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