Question

Considere a matriz A($a_{ij}$) de ordem 2 definida por

$a_{ij}$ = 2i + j, se i = j
i + 2j, se i ≠ j Calcule o determinante e marque a alternativa correta

a) -2 b) 8 c) 2 d) -8 c) 6

Answer 1

$Ola' \\ \\ Seja~a~matrix~de~ordem~2:\\ \begin{bmatrix}a_{11} &a_{12} \\ a_{21}&a_{22}\end{bmatrix}_{2_X2}~~~--\ \textgreater \ condic\~oes\begin{cases}a_{ij}=2i+j~,se~i=j \\ a_{ij}=i+2j~,se~i \neq j\end{cases} \\ \\ a_{11}=2(1)+1=3 \\ a_{12}=1+2(2)=5 \\ a_{21}=2+2(1)=4 \\ a_{22}=2(2)+2=6 \\ \\ \begin{bmatrix}3&5 \\ 4&6\end{bmatrix}_{2_X2} \\ \\ (3_X6)-(5_X4) \\ 18-20 \\\boxed{\boxed{ -2}}~---\ \textgreater \ resposta$

$\mathbb{nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn} \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$