Answer:
a) The simultaneous equation represented in matrix form, is
[1/3 1/4] [x] = [s]
[2/3 3/4] [y] = [w]
Ax = B
[1/3 1/4] = matrix A (matrix of coefficients)
[2/3 3/4]
[x] = matrix x (matrix of unknowns)
[y]
[s] = matrix B (matrix of answers)
[w]
b) Number of sick people the preceding week = 12005
Step-by-step explanation:
x = Number of sick people in a week
y = Number of people that are well in a week
s = Number of sick people the following week
w = Number of people that are well the following week.
The relationship between these is given as
(1/3)x + (1/4)y = s
(2/3)x + (3/4)y = w
In matrix form, this is simply presented as
[1/3 1/4] [x] = [s]
[2/3 3/4] [y] = [w]
which is more appropriately written as
Ax = B
where
[1/3 1/4] = matrix A (matrix of coefficients)
[2/3 3/4]
[x] = matrix x (matrix of unknowns)
[y]
[s] = matrix B (matrix of answers)
[w]
b) Taking the current conditions as s and w, then the preceding week will be x and y
The number of sick people in this week, s = 13000
The number of people well in this week, w = total population - Number of sick people.
w = 48000 - 13000 = 35000
So, the simultaneous equation becomes
(1/3)x + (1/4)y = 13000
(2/3)x + (3/4)y = 35000
Then we can solve for the number of sick and well people the preceding week.
We can solve normally or use matrix solution.
Ax = B
x, the matrix of unknowns is given by product of the inverse of A (inverse of the matrix of coefficients) and B (matrix of answers)
x = (A⁻¹)B
But, solving normally,
(1/3)x + (1/4)y = 13000
(2/3)x + (3/4)y = 35000
x = 12004.8 = 12005
y = 35995.2 = 35995
Number of sick people the preceding week = x = 12005
