Question

write a matlab code to solve this problem using Matlab below

Please make sure it works

Thank You

please use matrices

The following diagram shows part of the central section of UC Davis campus. Assume that the streets are one way, and that the average number of bikes entering and leaving this section during the 10 miutes breakes btween classes is given in the chart. Find the amount of the trafic between each of four intersection 250 120 120 70 West Quad X4 X2East Quad 175 ← 630 Shields Ave Solution; Assume that the number of bikes entering each intersection is equal to the number of the bikes leaving the intersection. For each intersection, this fact can be shown by an equation. +120 x 250 x3 + 115=x4 +175 +630 = x3 + 390 x+70-x2+ 120 Rewrite this system of lincar equations: +4 130 -240 -50 - 33 The augmented matrix of this system is -1 0 01 130 0 0 - 60 = 0 1-1 0-240 1-10 050 The row reduced cchclon form of this matrix is 10 0 - 130 01 0-1-180 Ao060 1 Rewrite this as a lincar system za = z. +-180 Since there is a free variable, this problem has many possible solutions, but >180 As an example if x400 the solution of the system will be r1 =530 P2 = 220 460

Answer 1

MATLAB Code:

close all
clear
clc

A = [-1 0 0 1;
0 0 1 -1;
0 1 -1 0;
1 -1 0 0]
b = [130; 60; -240; 50]
Ag = [A b] % Augmented Matrix
rref_Ag = rref(Ag) % Row reduced echelon form
fprintf('Rank(A) = Rank(Ag) = 3, but < 4 => Infinite number of solutions.\n')
fprintf('\tx1 = k - 130\n\tx2 = k - 180\n\tx3 = k + 60\n\tx4 = k (k = variable)\n')
fprintf('Eg: For k = 400\n')
k = 400;
fprintf('\tx1 = %d\n\tx2 = %d\n\tx3 = %d\n\tx4 = %d\n', k - 130, k - 180, k + 60, k)

Output:

A =
-1 0 0 1
0 0 1 -1
0 1 -1 0
1 -1 0 0
b =
130
60
-240
50
Ag =
-1 0 0 1 130
0 0 1 -1 60
0 1 -1 0 -240
1 -1 0 0 50
rref_Ag =
1 0 0 -1 -130
0 1 0 -1 -180
0 0 1 -1 60
0 0 0 0 0
Rank(A) = Rank(Ag) = 3, but < 4 => Infinite number of solutions.
   x1 = k - 130
   x2 = k - 180
   x3 = k + 60
   x4 = k (k = variable)
Eg: For k = 400
   x1 = 270
   x2 = 220
   x3 = 460
   x4 = 400