Question

Let A= ????

Answer 1

Answer

given,

A = $\begin{bmatrix}1 & 3 & 2\\3&1& 2\\4 & 3 & 2\end{bmatrix}$

B = $\begin{bmatrix}2 & 1 & 3\\ 2& 2& 1\\ 1 & 3 & 1\end{bmatrix}$

a) C = A + B

   C =$\begin{bmatrix}1 & 3 & 2\\3&1& 2\\ 4 & 3 & 2\end{bmatrix} +\begin{bmatrix}2 & 1 & 3\\ 2&2& 1\\ 1 & 3 & 1\end{bmatrix}$

   C = $\begin{bmatrix}1 +2 & 3+1 & 2+3\\3+2&1+2& 2+1\\ 4+1 & 3+2 & 2+1\end{bmatrix}$

   C = $\begin{bmatrix}3 & 4 & 5\\5&3& 3\\ 5& 5& 3\end{bmatrix}$

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 = $\begin{bmatrix}2 & 1 & 3\\ 2&2& 1\\ 1 & 3 & 1\end{bmatrix} + \begin{bmatrix}1 & 3 & 2\\3&1& 2\\ 4 & 3 & 2\end{bmatrix}$

   D =  $\begin{bmatrix}1 +2 & 3+1 & 2+3\\3+2&1+2& 2+1\\ 4+1 & 3+2 & 2+1\end{bmatrix}$

   D = $\begin{bmatrix}3 & 4 & 5\\5&3& 3\\ 5& 5& 3\end{bmatrix}$

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