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

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: