Question

Matriz
C 3x4, cij, = 3 ( i + j ) elevado a 2

Answer 1

Lembrando que "i" indica a linha e "j", a coluna de um elemento da matriz, temos:

$C~=~\left[\begin{array}{cccc}c_{11}&c_{12}&c_{13}&c_{14}\\c_{21}&c_{22}&c_{23}&c_{24}\\c_{31}&c_{32}&c_{33}&c_{34}\end{array}\right]\\\\\\\\C~=~\left[\begin{array}{cccc}3.(1+1)^2&3.(1+2)^2&3.(1+3)^2&3.(1+4)^2\\3.(2+1)^2&3.(2+2)^2&3.(2+3)^2&3.(2+4)^2\\3.(3+1)^2&3.(3+2)^2&3.(3+3)^2&3.(3+4)^2\end{array}\right]$

$C~=~\left[\begin{array}{cccc}3.(2)^2&3.(3)^2&3.(4)^2&3.(5)^2\\3.(3)^2&3.(4)^2&3.(5)^2&3.(6)^2\\3.(4)^2&3.(5)^2&3.(6)^2&3.(7)^2\end{array}\right]\\\\\\\\C~=~\left[\begin{array}{cccc}3.4&3.9&3.16&3.25\\3.9&3.16&3.25&3.36\\3.16&3.25&3.36&3.49\end{array}\right]$

$C~=~\left[\begin{array}{cccc}12&27&48&75\\27&48&75&108\\48&75&108&147\end{array}\right]$