Question

os elementos de uma matriz M quadrada de ordem 3x3 são dadas por aij, onde i+j, se i diferente de j 0 se i = j determine M+M​

Answer 1

Lembrando que "i" representa a linha e "j", a coluna de um elemento da matriz, temos:

$M~=~\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right]\\\\\\\\M~=~\left[\begin{array}{ccc}0&1+2&1+3\\2+1&0&2+3\\3+1&3+2&0\end{array}\right]\\\\\\\\M~=~\left[\begin{array}{ccc}0&3&4\\3&0&5\\4&5&0\end{array}\right]$

Calculando a soma M+M, temos:

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