Question

Seja= A (a) ij 3X3,Sendo:

aij= 1, se i > j
i + j, se i < j

O valor do determinante de A é igual a:

(A) 0. (B) 2. (C) 4. (D) 8.

quero cálculos alguém me ajude por favor ​

Answer 1

$\sf A=\left(\begin{array}{ccc} \sf a_{11}& \sf a_{12}& \sf a_{13} \\ \sf a_{21}& \sf a_{22}& \sf a_{23} \\ \sf a_{31}& \sf a_{32}& \sf a_{33} \end{array}\right)$

• $\sf a_{11}=1$

• $\sf a_{12}=1+1~\rightarrow~a_{12}=3$

• $\sf a_{13}=1+3~\rightarrow~a_{13}=4$

• $\sf a_{21}=1$

• $\sf a_{22}=1$

• $\sf a_{23}=2+3~\rightarrow~a_{23}=5$

• $\sf a_{31}=1$

• $\sf a_{32}=1$

• $\sf a_{33}=1$

Assim:

$\sf A=\left(\begin{array}{ccc} 1&3&4 \\ 1&1&5 \\ 1&1&1 \end{array}\right)$

$\sf det~(A)=1\cdot1\cdot1+3\cdot5\cdot1+4\cdot1\cdot1-1\cdot1\cdot4-1\cdot5\cdot1-1\cdot1\cdot3$

$\sf det~(A)=1+15+4-4-5-3$

$\sf det~(A)=20-12$

$\sf det~(A)=8$

Letra D