Question

Sendo A=(aij)4x3 com aij=j ,B=(bji)4x3 com bij=2.i e C=2A+b, então o elemento C32 da matriz C é igual a

Answer 1

 De acordo com o enunciado,

$A=\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\a_{41}&a_{42}&a_{43}\end{bmatrix}\Rightarrow\,A=\begin{bmatrix}1&2&3\\1&2&3\\1&2&3\\1&2&3\end{bmatrix}$

 E,

$B=\begin{bmatrix}b_{11}&b_{12}&b_{13}\\b_{21}&b_{22}&b_{23}\\b_{31}&b_{32}&b_{33}\\b_{41}&b_{42}&b_{43}\end{bmatrix}\Rightarrow\,B=\begin{bmatrix}2&2&2\\4&4&4\\6&6&6\\8&8&8\end{bmatrix}$

 Por conseguinte,

$C=\begin{bmatrix}c_{11}&c_{12}&c_{13}\\c_{21}&c_{22}&c_{23}\\c_{31}&c_{32}&c_{33}\\c_{41}&c_{42}&c_{43}\end{bmatrix}=\\\\\\C=\begin{bmatrix}c_{11}&c_{12}&c_{13}\\c_{21}&c_{22}&c_{23}\\c_{31}&2\cdot2+6&c_{33}\\c_{41}&c_{42}&c_{43}\end{bmatrix}$

 Daí,

$C_{32}=4+6\\\\\boxed{C_{32}=10}$