Question

Determinantes:
SEJA: A= (aij) 3x3 , em que o
(aij)= (i-j)²??

Answer 1

Olá,

a matriz A = (aij) 3X3, possui matriz genérica $A= \left(\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right)$

se aij=(i - j)², então A é igual..

$A= \left(\begin{array}{ccc}(1-1)^2&(1-2)^2&(1-3)^2\\(2-1)^2&(2-2)^2&(2-3)^2\\(3-1)^2&(3-2)^2&(3-3)^2\end{array}\right)\\\\\\ A= \left(\begin{array}{ccc}0^2&(-1)^2&(-2)^2\\1^2&0^2&(-1)^2\\2^2&1^2&0^2\end{array}\right)\\\\\\ \huge\boxed{A= \left(\begin{array}{ccc}0&1&4\\1&0&1\\4&1&0\end{array}\right)}$

Tenha ótimos estudos ;D