Question

Dada a matriz C = (Cij)3x3 definida por Cij = 2i - j, determine a soma dos elementos da diagonal secundária. 

A) 9
C) 11
D) 10
E) 7
F) 6
​

Answer 1

Resposta:

(F) 6

Explicação passo a passo:

$\left[\begin{array}{ccc}c_{11}&c_{12}&c_{13}\\c_{21}&c_{22}&c_{23}\\c_{31}&c_{32}&c_{33}\end{array}\right] =\left[\begin{array}{ccc}.[(2*1)-1]&[(2*1)-2]&[(2*1)-3]\\.[(2*2)-1]&[(2*2)-2]&[(2*2)-3]\\.[(2*3)-1]&[(2*3)-2]&[(2*3)-3]\end{array}\right]=$

$\left[\begin{array}{ccc}(2-1)&(2-2)&(2-3)\\(4-1)&(4-2)&(4-3)\\(6-1)&(6-2)&(6-3)\end{array}\right]=\left[\begin{array}{ccc}1&0&-1\\3&2&1\\5&4&3\end{array}\right]$

Portanto, a soma dos elementos da diagonal secundária da matriz C é:

$\left[\begin{array}{ccc}1&0&-1\\3&2&1\\5&4&3\end{array}\right]=\left[\begin{array}{ccc}1&0&-1\\3&2&1\\5&4&3\end{array}|\begin{array}{cc}1&0\\3&2\\5&4\end{array}\right]=(0*3*3)+(1*1*4)+(-1*2*5)\\\\\\=0+4+(-10)=4-10=-6$

Invertendo o sinal, assim, o valor da soma da diagonal secundária vale 6.