Matemática, perguntado por douglasbottan, 4 meses atrás

Escreva a matriz A=(aij) 5x3, tal que aij= 3i-2j +4

Soluções para a tarefa

Respondido por solkarped

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

$\Large\displaystyle\text{$\begin{gathered} A = \begin{bmatrix}5 & 3 & 1\\8 & 6 & 4\\11 & 9 & 7\\14 & 12 & 10\\ 17 & 15 & 13\end{bmatrix}\end{gathered}$}$

Seja a lei de formação da matriz:

$\Large\displaystyle\text{$\begin{gathered} A = (a_{ij})_{5\times3}\:\:\textrm{tal que}\:\:a_{ij} = 3i - 2j + 4\end{gathered}$}$

Montando a referida matriz, temos:

$\Large\displaystyle\text{$\begin{gathered} 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}\\a_{51} & a_{52} & a_{53}\end{bmatrix}\end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered} = \begin{bmatrix} 3\cdot1 - 2\cdot1 + 4 & 3\cdot1 - 2\cdot2 + 4 & 3\cdot1 - 2\cdot3 + 4\\3\cdot2 - 2\cdot1 + 4 & 3\cdot2 - 2\cdot2 + 4 & 3\cdot2 - 2\cdot3 + 4\\3\cdot3 - 2\cdot1 + 4 & 3\cdot3 - 2\cdot2 + 4 & 3\cdot3 - 2\cdot3 + 4\\3\cdot4 - 2\cdot1 + 4 & 3\cdot4 - 2\cdot2 + 4 & 3\cdot4 - 2\cdot3 + 4\\3\cdot5 - 2\cdot1 + 4 & 3\cdot5 - 2\cdot2 + 4 & 3\cdot5 - 2\cdot3 + 4\end{bmatrix}\end{gathered}$}$

$\Large\displaystyle\text{$\begin{gathered} = \begin{bmatrix} 3 - 2 + 4 & 3 - 4 + 4 & 3 - 6 + 4\\6 - 2 + 4 & 6 - 4 + 4 & 6 - 6 + 4\\9 - 2 + 4 & 9 - 4 + 4 & 9 - 6 + 4\\12 - 2 + 4 & 12 - 4 + 4 & 12 - 6 + 4\\15 - 2 + 4 & 15 - 4 + 4 & 15 - 6 + 4\end{bmatrix}\end{gathered}$}$

$\Large\displaystyle\text{$\begin{gathered} = \begin{bmatrix}5 & 3 & 1\\8 & 6 & 4\\11 & 9 & 7\\14 & 12 & 10\\ 17 & 15 & 13\end{bmatrix}\end{gathered}$}$

✅ Portanto a matriz procurada é:

$\Large\displaystyle\text{$\begin{gathered} A = \begin{bmatrix}5 & 3 & 1\\8 & 6 & 4\\11 & 9 & 7\\14 & 12 & 10\\ 17 & 15 & 13\end{bmatrix}\end{gathered}$}$

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