Question

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

Answer 1

Resposta:

S=x₁₁+x₂₂+x₃₃=3

Explicação passo a passo:

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

$\left[\begin{array}{ccc}2-2&9-7&7-2\\-1-8&7+1&10+3\\5+1&1-9&0-5\end{array}\right] =\left[\begin{array}{ccc}x_{11}&x_{12}&x_{13}\\x_{21}&x_{22}&x_{23}\\x_{31}&x_{32}&x_{33}\end{array}\right]$

A diagonal primária da matriz x:

x₁₁=2-2=0

x₂₂=7+1=8

x₃₃=0-5= -5

A soma (S):

S=x₁₁+x₂₂+x₃₃=0+8-5=3