Question

PROBLEM 3. points 30 Use MATL.AB You are given the following cquations of r, y, z as functions of the parametcr c 7x +3y-52 13 1. points 5 Use MATLAB's built-in function linsolve under the symbolic mode syms to solve the above system 3. Your solutions will be functions of c. using a for loop programming structure. Take steps of 0.5. plot, for 10 cs 10. Comment on the results. 2. points 20 Solve numerically the system 3 for different values of c where -10 c 10 3. points 5 Plot the solutions for r, y,z versus e from questions 1 and 2 above, on the same

Answer 1

Contents

close all
clc
clear all
%

Questuion 1

syms c % C as a constant
A = [ c -5  -2;
     6 3 c;
     7 3 -5 ];
B = [11; 13; 13];
X = linsolve(A,B) % Solution of system 3
%
%%Question 2 and Question 3
for c = -10:0.5:10 % Step value of c having 0.5 from -10 to 10
    A = [ c -5  -2;
     6 3 c;
     7 3 -5 ];
B = [11; 13; 13];
X = linsolve(A,B)
figure(1)
plot(X(1),c,'.');
hold on
figure(2)
plot(X(2),c,'.');
hold on
figure(3)
plot(X(3),c,'.');
hold on
end

 
X =
 
             (98*(c + 5))/(3*c^2 + 50*c + 144)
 -(- 13*c^2 + 12*c + 356)/(3*c^2 + 50*c + 144)
                       98/(3*c^2 + 50*c + 144)
 

X =

    8.7500
  -19.0000
   -1.7500


X =

    7.3195
  -15.4564
   -1.6266


X =

    6.2222
  -12.7778
   -1.5556


X =

    5.3385
  -10.6654
   -1.5253


X =

    4.5937
   -8.9375
   -1.5313


X =

    3.9357
   -7.4739
   -1.5743


X =

    3.3220
   -6.1864
   -1.6610


X =

    2.7097
   -5.0000
   -1.8065


X =

    2.0417
   -3.8333
   -2.0417


X =

    1.2174
   -2.5652
   -2.4348


X =

   -0.0000
   -0.9355
   -3.1613


X =

   -2.4198
    1.9136
   -4.8395


X =

  -12.2500
   12.5000
  -12.2500


X =

   25.5652
  -26.9130
   17.0435


X =

    9.3333
   -9.6667
    4.6667


X =

    6.4901
   -6.4834
    2.5960


X =

    5.2500
   -5.0000
    1.7500


X =

    4.5281
   -4.0759
    1.2937


X =

    4.0412
   -3.4124
    1.0103


X =

    3.6827
   -2.8956
    0.8184


X =

    3.4028
   -2.4722
    0.6806


X =

    3.1753
   -2.1134
    0.5773


X =

    2.9848
   -1.8020
    0.4975


X =

    2.8217
   -1.5271
    0.4341


X =

    2.6797
   -1.2813
    0.3828


X =

    2.5543
   -1.0591
    0.3406


X =

    2.4424
   -0.8567
    0.3053


X =

    2.3415
   -0.6711
    0.2755


X =

    2.2500
   -0.5000
    0.2500


X =

    2.1664
   -0.3415
    0.2280


X =

    2.0896
   -0.1940
    0.2090


X =

    2.0186
   -0.0564
    0.1923


X =

    1.9529
    0.0725
    0.1775


X =

    1.8917
    0.1935
    0.1645


X =

    1.8346
    0.3073
    0.1529


X =

    1.7812
    0.4148
    0.1425


X =

    1.7310
    0.5163
    0.1332


X =

    1.6837
    0.6125
    0.1247


X =

    1.6392
    0.7037
    0.1171


X =

    1.5971
    0.7904
    0.1101


X =

    1.5572
    0.8729
    0.1038

figure 1

X axis - c

Y axis - Value of x

10 -2 4 6 -8 -10 15 -10 5 05 1015 20 25 30

figure 2

X axis - c

Y axis - Value of y

10 8 6 4 2 0 -2 -4 -6 -8 -10 -30 -25 20 15 10 -505 10 5

figure 3

X axis - c

Y axis - Value of z

5 0 5 10 2-4-6-8-10 86420

From all the graph we can say that about c = - 3.5 the graph pattern start differentiating.