Question

Sendo a matriz A = (aij) tal que aij = i -j, o valor de 31 + a22 é: ajuda pfv

Answer 1

✅ Após montarmos a matriz e resolver a situação, concluímos que o valor procurado é:

           $\large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf V = 31\:\:\:}} \end{gathered} }$

Seja a matriz quadrada de ordem 3x3:

      $\Large\displaystyle\begin{gathered}A_{3x3} = a_{ij}\:\:\:tal\:que\:\:\:a_{ij} = i - j \end{gathered}$

Então temos:

    $\large\displaystyle\begin{gathered}A = \begin{pmatrix}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\a_{31} & a_{32} & a_{33} \end{pmatrix} \end{gathered}$

         $\large\displaystyle\begin{gathered}= \begin{pmatrix}1-1 & 1- 2 & 1-3\\2-1 & 2-2 & 2-3\\3-1 & 3-2 & 3-3 \end{pmatrix}\end{gathered}$

         $\large\displaystyle\begin{gathered}= \begin{pmatrix}0 & -1 & -2\\1 & 0 & -1\\2 & 1 & 0 \end{pmatrix}\end{gathered}$

Se:

            $\large\displaystyle\begin{gathered}a_{22} = 0 \end{gathered}$

Então, temos:

          $\large\displaystyle\begin{gathered}V = 31 + a_{22} \end{gathered}$

              $\large\displaystyle\begin{gathered}= 31 + 0 \end{gathered}$

              $\large\displaystyle\begin{gathered}= 31 \end{gathered}$

✅ Portanto, o valor procurado é:

          $\large\displaystyle\begin{gathered}V = 31 \end{gathered}$

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