Question

Encontre os valores dos elementos da matriz A 3x4
onde aij = i^2 + j^3​

Answer 1

$A~=~\left[\begin{array}{cccc}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\a_{31}&a_{32}&a_{33}&a_{34}\end{array}\right]\\\\\\\\A~=~\left[\begin{array}{cccc}1^2+1^3&1^2+2^3&1^2+3^3&1^2+4^3\\2^2+1^3&2^2+2^3&2^2+3^3&2^2+4^3\\3^2+3^3&3^2+2^3&3^2+3^3&3^2+4^3\end{array}\right]$

$A~=~\left[\begin{array}{cccc}1+1&1+8&1+27&1+64\\4+1&4+8&4+27&4+64\\9+1&9+8&9+27&9+64\end{array}\right]\\\\\\\\A~=~\left[\begin{array}{cccc}2&9&28&65\\5&12&31&68\\10&17&36&73\end{array}\right]$

Answer 2

Explicação passo-a-passo:

Essa é uma matriz retangular 3 x 4 (3 linhas e 4 colunas)

    $A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{array}\right\left\begin{array}{ccc}a_{14}\\a_{24}\\a_{34}\end{array}\right]$

Se $a_{ij}=i^{2}+j^{3}$, então:

    $a_{11}=1^{2}+1^{3}=1+1=2$

    $a_{12}=1^{2}+2^{3}=1+8=9$

    $a_{13}=1^{2}+3^{3}=1+27=28$

    $a_{14}=1^{2}+4^{3}=1+64=65$

    $a_{21}=2^{2}+1^{3}=4+1=5$

    $a_{22}=2^{2}+2^{3}=4+8=12$

    $a_{23}=2^{2}+3^{3}=4+27=31$

    $a_{24}=2^{2}+4^{3}=4+64=68$

    $a_{31}=3^{2}+1^{3}=9+1=10$

    $a_{32}=3^{2}+2^{3}=9+8=17$

    $a_{33}=3^{2}+3^{3}=9+27=36$

    $a_{34}=3^{2}+4^{3}=9+64=73$

Daí,

          $A=\left[\begin{array}{ccc}2&9&28\\5&12&31\\10&17&36\end{array}\right\left\begin{array}{ccc}65\\68\\73\end{array}\right]$