Question

Obter a matriz A = (aij)2×2 definida por aij = 2 i –2 j.

Answer 1

$A=\left(a_{ij}\right)_{2\times2}\Longrightarrow A=\left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]\Longrightarrow a_{ij}=2(i-j)$

$a_{11}=2(1-1)\ \therefore\ \boxed{a_{11}=0}$

$a_{12}=2(1-2)\ \therefore\ \boxed{a_{12}=-2}$

$a_{21}=2(2-1)\ \therefore\ \boxed{a_{21}=2}$

$a_{22}=2(2-2)\ \therefore\ \boxed{a_{22}=0}$

$\boxed{A=\left[\begin{array}{cc}0&-2\\2&0\end{array}\right]}$