Mathematics: Let a= 1 3 2 3 1 2 4 3 2 and b = 2 1 3 2 2 1 1 3 1 represent the bus routes of two companies between three cities. a. let c = a+ b. find matrix c. explain what the resulting matrix and entry c1,3 mean in this context. b. let d = b + a. find matrix d. explain what the resulting matrix and entry ,3 mean in this context. c. what is the relationship between matrices c and d? why do you think that is?

That’s a piece of paper right there...

Let a= 1 3 2 3 1 2 4 3 2 and b = 2 1 3 2 2 1 1 3 1 - id132312432213221133397213, jvanegas6797

nikejose11

07.01.2022

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

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