Question

ache os elementos da matriz A= (aij) de ordem 3, em que aij= i2+ j2

Answer 1

$\left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\end{array}\right]$

$\left[\begin{array}{ccc}1^2+1^2&1^2+2^2&1^2+3^2\\2^2+1^2&2^2+2^2&2^2+3^2\\3^2+1^2&3^2+2^2&3^2+3^2\end{array}\right] = \left[\begin{array}{ccc}2&5&10\\5&8&13\\10&13&18\end{array}\right]$

Answer 2

Uma matriz de ordem 3, tal que:

$A= \left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\end{array}\right]$

Agora basta achar cada um:

$a11 = 1^2 + 1^2 = 2 \\ \\ a12=1^2+2^2=5 \\ \\ a13=1^2+3^2=10 \\ \\ a21=2^2 + 1^2=5 \\ \\ a22=2^2+2^2=8 \\ \\ a23=2^2+3^2=13 \\ \\ a31= 3^2+1^2=10 \\ \\ a32=3^2+2^2=13 \\ \\ a33=3^2+3^2=18$

Sabendo o valor de cada um:

$A= \left[\begin{array}{ccc}2&5&10\\5&8&13\\10&13&18\end{array}\right]$