Question

Determine a soma dos elementos da matiz A = $(a_{ij}) _{2x2}$, tal que $a_{ij} = (-1)^{i+j}$.

Answer 1

$a11 = {( - 1 )}^{1 + 1} = {( - 1)}^{2} = ( - 1) \times ( - 1) = 1$
$a12 = {( - 1)}^{1 + 2} = {( - 1)}^{3} = ( - 1) \times ( - 1) \times ( - 1) = - 1$
$a21 = {( - 1)}^{2 + 1} = {( - 1)}^{3} = ( - 1) \times ( - 1) \times ( - 1) = - 1$
$a22 = {( - 1)}^{2 + 2} = {( - 1)}^{4} = ( - 1) \times ( - 1) \times ( - 1) \times ( - 1) = + 1$
-1-1+1+1=0