Question

Seja a matriz b= (bij) 3×2, em que bij=3. (i+j)2. Determine a matriz respeitando essas condições

Answer 1

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

      $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf B = \begin{bmatrix} 12 & 27\\27 & 48\\48 & 75\end{bmatrix}\:\:\:}}\end{gathered} }$

Seja a matriz cuja lei de formação é:

     $\Large\displaystyle\begin{gathered} B = (b_{ij})_{3\times2}\:\textrm{tal que}\:b_{ij} = 3\cdot(i + j)^{2}\end{gathered}$

Montando a referida matriz:

      $\Large\displaystyle\begin{gathered} B = \begin{bmatrix}a_{11} & a_{12}\\ a_{21} & a_{22}\\a_{31} & a_{32}\end{bmatrix} \end{gathered}$

            $\Large\displaystyle\begin{gathered} = \begin{bmatrix} 3\cdot(1 + 1)^{2} & 3\cdot(1 + 2)^ {2}\\3\cdot(2 + 1)^{2} & 3\cdot(2 + 2)^{2}\\3\cdot(3 + 1)^{2} & 3\cdot(3 + 2)^{2}\end{bmatrix} \end{gathered}$

            $\Large\displaystyle\begin{gathered} = \begin{bmatrix} 3\cdot2^{2} & 3\cdot3^{2}\\3\cdot3^{2} & 3\cdot4^{2}\\3\cdot4^{2} & 3\cdot5^{2}\end{bmatrix} \end{gathered}$

            $\Large\displaystyle\begin{gathered} = \begin{bmatrix} 3\cdot4 & 3\cdot 9\\3\cdot 9 & 3\cdot16\\3\cdot16 & 3\cdot25\end{bmatrix} \end{gathered}$

            $\Large\displaystyle\begin{gathered} = \begin{bmatrix} 12 & 27\\27 & 48\\48 & 75\end{bmatrix} \end{gathered}$

✅ Portanto, a matriz procurada é:

       $\Large\displaystyle\begin{gathered} B = \begin{bmatrix} 12 & 27\\27 & 48\\48 & 75\end{bmatrix} \end{gathered}$

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

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