Question

me ajude calcular soma das matrizes

Answer 1

Resposta:

$C=\left[\begin{array}{ccc}5&9&15\\8&12&18\\11&15&21\end{array}\right]$

Explicação passo-a-passo:

Para calcular

$A+B=C$

Temos que calcular as matrizes $A$ e $B$.

$A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right]$

Onde cada elemento $a_{ij}$ vale $i+j^2$, isto é,

$A=\left[\begin{array}{ccc}1+1^2&1+2^2&1+3^2\\2+1^2&2+2^2&2+3^2\\3+1^2&3+2^2&3+3^2\end{array}\right]$

$A=\left[\begin{array}{ccc}1+1&1+4&1+9\\2+1&2+4&2+9\\3+1&3+4&3+9\end{array}\right]$

$A=\left[\begin{array}{ccc}2&5&10\\3&6&11\\4&7&12\end{array}\right]$

No caso da matriz $B$,

$B=\left[\begin{array}{ccc}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\end{array}\right]$

Temos que cada $b_{ij}$ vale $2i+j$, ou seja,

$B=\left[\begin{array}{ccc}2\cdot1+1&2\cdot1+2&2\cdot1+3\\2\cdot2+1&2\cdot2+2&2\cdot2+3\\2\cdot3+1&2\cdot3+2&2\cdot3+3\end{array}\right]$

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

$B=\left[\begin{array}{ccc}3&4&5\\5&6&7\\7&8&9\end{array}\right]$

Agora vamos calcular a matriz $C$

$A+B=C$

$C=\left[\begin{array}{ccc}2&5&10\\3&6&11\\4&7&12\end{array}\right] +\left[\begin{array}{ccc}3&4&5\\5&6&7\\7&8&9\end{array}\right]$

$C=\left[\begin{array}{ccc}2+3&5+4&10+5\\3+5&6+6&11+7\\4+7&7+8&12+9\end{array}\right]$

$C=\left[\begin{array}{ccc}5&9&15\\8&12&18\\11&15&21\end{array}\right]$