Question

Determine o valor da soma de todos os elementos da diagonal secundária da matriz X.

17
16
20
18
19​

Answer 1

Resposta:

A soma de todos os elementos da diagonal secundária da matriz X vale 19

Explicação passo-a-passo:

Diagonal secundária: x₁₃, x₂₂ e x₃₁

$\left[\begin{array}{ccc}-1&4&5\\0&2&7\\1&-1&-2\end{array}\right]+\left[\begin{array}{ccc}3&5&2\\-1&5&3\\4&2&2\end{array}\right] =\left[\begin{array}{ccc}x_{11}&x_{12}&x_{13}\\x_{21}&x_{22}&x_{23}\\x_{31}&x_{32}&x_{33}\end{array}\right] +\left[\begin{array}{ccc}2&7&2\\8&-1&-3\\-1&9&5\end{array}\right]$$\left[\begin{array}{ccc}-1+3&4+5&5+2\\0-1&2+5&7+3\\1+4&-1+2&-2+2\end{array}\right] =\left[\begin{array}{ccc}x_{11}+2&x_{12}+7&x_{13}+2\\x_{21}+8&x_{22}-1&x_{23}-3\\x_{31}-1&x_{32}+9&x_{33}+5\end{array}\right]$

Comparando os elementos da diagonal secundária:

x₁₃+2= 5+2 => x₁₃=5

x₂₂-1=2+5 => x₂₂=8

x₃₁-1= 1+4 => x₃₁= 6

x₁₃+x₂₂+x₃₁=5+8+6=19