Question

Determine os elementos da matriz Cij2×2 onde Cij=i²×j²+3

Answer 1

✅ Após resolver os cálculos, concluímos que a matriz quadrada procurada é:

                   $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf C = \begin{bmatrix} 4 & 7\\7 & 19\end{bmatrix}\:\:\:}}\end{gathered} }$

Seja a matriz, cuja lei de formação é:

        $\Large\displaystyle\begin{gathered} C_{2\times2} = c_{ij},\:\:\textrm{tal que}\:\:c_{ij} = i^{2}\cdot j^{2} + 3\end{gathered}$

Então, temos:

       $\Large\displaystyle\begin{gathered}C = \begin{bmatrix} c_{11} & c_{12}\\c_{21} & c_{22}\end{bmatrix}\end{gathered}$

             $\Large\displaystyle\begin{gathered} = \begin{bmatrix} 1^{2}\cdot1^{2} + 3 & 1^{2}\cdot2^{2} + 3\\2^{2}\cdot1^{2} + 3 & 2^{2}\cdot2^{2} + 3\end{bmatrix}\end{gathered}$

             $\Large\displaystyle\begin{gathered}= \begin{bmatrix} 1\cdot1 + 3 & 1 \cdot4 + 3\\4\cdot1 + 3 & 4\cdot4 + 3\end{bmatrix}\end{gathered}$

             $\Large\displaystyle\begin{gathered}= \begin{bmatrix} 1 + 3 & 4 + 3\\4 + 3 & 16 + 3\end{bmatrix}\end{gathered}$

              $\Large\displaystyle\begin{gathered}= \begin{bmatrix} 4 & 7\\7 & 19\end{bmatrix}\end{gathered}$

✅ Portanto, a matriz procurada é:

         $\Large\displaystyle\begin{gathered}C = \begin{bmatrix} 4 & 7\\7 & 19\end{bmatrix}\end{gathered}$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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