Question

escreva a matriz A=(aij) do tipo 3x4 sabendo que aij=2i-3j

Answer 1

$A=(a_{ij})_{3X4}~|~a_{ij}=2i-3j\\\\\\\text{Onde o \'indice i representa linhas, e o \'indice j representa colunas.}$


$a_{11}=2\cdot 1-3\cdot 1=2-3=-1\\a_{21}=2\cdot 2-3\cdot 1=4-3=1\\a_{31}=2\cdot 3-3\cdot 1=6-3=3\\\\\\a_{12}=2\cdot 1-3\cdot 2=2-6=-4\\a_{22}=2\cdot 2-3\cdot 2=4-6=-2\\a_{32}=2\cdot 3-3\cdot 2=6-6=0\\\\\\a_{13}=2\cdot 1-3\cdot 3=2-9=-7\\a_{23}=2\cdot 2-3\cdot 3=4-9=-5\\a_{33}=2\cdot 3-3\cdot 3=6-9=-3\\\\\\a_{14}=2\cdot 1-3\cdot 4=2-12=-10\\a_{24}=2\cdot 2-3\cdot 4=4-12=-8\\a_{34}=2\cdot 3-3\cdot 4=6-12=-6$


$\text{Substituindo os dados na matriz:}\\\\\\\ A=\large\begin{pmatrix} a_{11} &a_{12}&a_{13}&a_{14}\\ a_{21}&a_{22}&a_{23}&a_{24}\\ a_{31}&a_{32}&a_{33}&a_{34} \end{pmatrix}\\\\\\ A=\begin{pmatrix} -1&-4&-7&-10\\ 1&-2&-5&-8\\ 3&0&-3&-6\end{pmatrix}$