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?

Answer

given,

A =

B =

a) C = A + B

   C =

   C =

   C =

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 =

   D =  

   D =

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

50 min

step-by-step explanation:

they will be decreasing both their times in half

60 / 2 = 30

40/2 = 20

30 + 20 = 50

0 is its x and y coordinate