Question

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

Answer 1

Bom dia!

Note que na diagonal principal os valores serão zero:

$\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right] \ \rightarrow \ M= \left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right]$

M + M:

$M+M= \left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right] + \left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right] = \left[\begin{array}{ccc}0+0&3+3&4+4\\3+3&0+0&5+5\\4+4&5+5&0+0\end{array}\right] \\ M+M= \left[\begin{array}{ccc}0&6&8\\6&0&10\\8&10&0\end{array}\right]$