Question

Perform the following tasks/questions in separate MATLAB cells (label cells as task/question numbers). Note the first cell (unnumbered) should be your Name, section number and the version of this Assignment. Tasks follow:

Perform the following tasks/questions in separate MATLAB cells (label cells as task/question numbers). Note the first cell (unnumbered) should be your Name, section number and the version of this Assignment. Tasks follow: Consider the following system of linear equations: -3x, +x2 4x32 2x1 - 3xz 4x34 which could represent the constant voltages in a circuit, or the static forces in a bridge. The coefficient "k" is a parameter of the system under consideration that can vary Perform the following tasks (label cells as task numbers). Note the first cel (unnumbered) should be your Name, section number and the version of this Assignment. Tasks follow: 1· Let k = 7 and enter the system into MATLAB as an augmented matrix. What kind of solution does this system have (if it has one)? Justify your answer as comments in cell. 2. Let k-4:0.05:6.90 and create a for loop that finds and saves the solution of the system for each value of k. DO THIS BY INDEXING Here are a few hints to help Use the numel function to find out how many elements are in k Use the zeros function to create a place to store your solutions call it results Each solution of the system is a 3x column vector, so the matrix called results must be 3xN, where N is the number of elements in k a. b. Let w be the indexing variable used in the for loop c. i. For each pass through the loop run, extract the wh value from k, and substitute it into the system augmented matrix (location M(1,1), find the solution using RREF (remember last column is solution) ii. iii. extract the 3x1 solution vector and store it in the w column of your solution matrix (results). 3. Plot all three components of the system solution versus k. Discuss what the graph look like as k approaches 7? Does this make sense? Correct plot is given below Solution of linear equations vs k VersionA

Answer 1

Please find required MATLAB code along with necessary details in comments:

clear all; clc; close all;

k=[4:0.05:6.90]; % possible values of k
N=numel(k); % number of elements in k
results=zeros(3,N); % initial matrix for storing results
for w=1:N
kval=k(w);   
% given matrix of A
A=[kval 0 -16 9; -3 1 4 -2; 2 -3 4 -4];
temp=rref(A); % find the solution
results(:,w)=temp(:,end);   
end
% Plot the data
plot(k,results(1,:),'b-');
hold on
plot(k,results(2,:),'r-');
plot(k,results(3,:),'m-');
legend('x_0','x_1','x_2');
xlabel('k'); ylabel('variables x_0, x_1, x_2')

==================== SCREENSHOT OF CODE

main-script.m ×1+ clear all clc: close all: 烂[4 : 0 . 05: 6·90] ; N=numel (k) ; results=zeros (3,N); for w=1 : N 롬 possible values of k % number of elements in k ⅝ initial matrix for storing results kval=k (W) ; given matrix of A A-kval 0-16 9;-314-2; temp=rref (A) ; results(,w)tp,end): 2-34-4); 10 % find the solution 12 - 13 end Plot the data plot (k, results (1, ),-'); hold on plot (k, results (2,:), 'r-'); plot (k, results (3, '); legend 'x 0''x 1', 'x 2') xlabel ('k' ); ylabel ('variables x 0, x 1, x 2') 15 16 18

========================== SAMPLE OUTPUT

7 6 .5 k 5 4 0 6 4