Question

Determine a matriz quadrada de ordem 2 de acordo com a lei abaixo

Answer 1

$\Large\boxed{\begin{array}{l}\rm A=[a_{ij}]_{2\times2},~com\,a_{ij}=(-1)^{i+j}\cdot i\cdot j\\\rm a_{11}=(-1)^{1+1}\cdot1\cdot1=1\\\rm a_{12}=(-1)^{1+2}\cdot1\cdot2=-2\\\rm a_{21}=(-1)^{2+1}\cdot2\cdot1=-2\\\rm a_{22}=(-1)^{2+2}\cdot2\cdot2=4\\\\\rm A=\begin{bmatrix}\rm\,\,\,\,1&\rm-2\\\rm-2&\rm\,\,\,\,4\end{bmatrix}\end{array}}$