Question

Dada a matriz A = (aij)2 x 2, em que aij = 2.i + j, calcule o det. (A).

Answer 1

Explicação passo-a-passo:

$\sf A=\left(\begin{array}{cc} \sf a_{11}& \sf a_{12} \\ \sf a_{21}& \sf a_{22} \end{array}\right)$

• $\sf a_{ij}=2i+j$

• $\sf a_{11}=2\cdot1+1~\rightarrow~a_{11}=2+1~\rightarrow~a_{11}=3$

• $\sf a_{12}=2\cdot1+2~\rightarrow~a_{12}=2+2~\rightarrow~a_{12}=4$

• $\sf a_{21}=2\cdot2+1~\rightarrow~a_{21}=4+1~\rightarrow~a_{21}=5$

• $\sf a_{22}=2\cdot2+2~\rightarrow~a_{22}=4+2~\rightarrow~a_{22}=6$

Assim:

$\sf A=\left(\begin{array}{cc} 3&4 \\ 5&6 \end{array}\right)$

$\sf det~(A)=3\cdot6-4\cdot5$

$\sf det~(A)=18-20$

$\sf det~(A)=-2$