Respuesta :
Answer
given,
A = [tex]\begin{bmatrix}1 & 3 & 2\\3&1& 2\\4 & 3 & 2\end{bmatrix}[/tex]
B = [tex]\begin{bmatrix}2 & 1 & 3\\ 2& 2& 1\\ 1 & 3 & 1\end{bmatrix}[/tex]
a) C = A + B
C =[tex]\begin{bmatrix}1 & 3 & 2\\3&1& 2\\ 4 & 3 & 2\end{bmatrix} +\begin{bmatrix}2 & 1 & 3\\ 2&2& 1\\ 1 & 3 & 1\end{bmatrix}[/tex]
C = [tex]\begin{bmatrix}1 +2 & 3+1 & 2+3\\3+2&1+2& 2+1\\ 4+1 & 3+2 & 2+1\end{bmatrix}[/tex]
C = [tex]\begin{bmatrix}3 & 4 & 5\\5&3& 3\\ 5& 5& 3\end{bmatrix}[/tex]
the resulting matrix represent the cities and the route in a single matrix of both the company together.
C₁ ₃ = means city 1 have routes
so, C₁ ₃ = 5
b) D = B + A
D = [tex]\begin{bmatrix}2 & 1 & 3\\ 2&2& 1\\ 1 & 3 & 1\end{bmatrix} + \begin{bmatrix}1 & 3 & 2\\3&1& 2\\ 4 & 3 & 2\end{bmatrix}[/tex]
D = [tex]\begin{bmatrix}1 +2 & 3+1 & 2+3\\3+2&1+2& 2+1\\ 4+1 & 3+2 & 2+1\end{bmatrix}[/tex]
D = [tex]\begin{bmatrix}3 & 4 & 5\\5&3& 3\\ 5& 5& 3\end{bmatrix}[/tex]
D₁ ₃ = means the value of the element on the first row and third column
so, D₁ ₃ = 5
c) both the matrix represent same value
we can say that matrix addition follows commutative law
A + B = B + C
