Question

Please answer these Matlab questions when able. Thanks.

4. Laboratory Problem Description In this laboratory you are required to find eigenvalue and eigenvectors for A in the following systems of linear equation Ax-B: 17x1+2x2+3x3+4x44 5x1+6x2+7x3+8x4 3 9x1+10x2+11x3+12x4 2 13x1+14x2+15x3+16x4 1 Apply the following commands: >>A 1 12:211 Verify that the columns of X in the example above indeed are eigenvectors to the matrix A. In other words, multiply (using Matlab) the matrix A to the columns (one at a time) of X and check that they are eigenvectors corresponding to the eigenvalues. Compute characteristic polynomial for A-2 3 1-1 23,012] 5. Laboratory Exercises EX1: Given the following matrix: A-1 0 3 1 2 3 Using MATLAB commands find the following: O The eigenvalues of matrix A O The eigenvectors of matrix A EX2: Find the characteristic polynomial for A in EX1

Answer 1

`Hey,

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4)

clc
clear all
close all
A=[17,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16];
[X,D]=eig(A);
Vec=diag(D);
for i=1:4
fprintf('For %d eigen vector\n',i);
disp('A*eigen vector');
disp(A*X(:,i))
disp('eigenvalue*X=');
Vec(i)*X(:,i)
end

MATLAB R2014a HOME PLOTS EDITOR Find Files Compare Print Comment Go To New Open Save Breakpoints Run Run and Advance Advance Run and Indent Ele , i Find - Time C: Users PRADEEP KALRA 、Documents MATLAB Current Folder Editor-CAUsers)PRADEEP KALRALDocuments)MATLABlsaveee.m secantbypradeep.m bisectionmethodbypradeep.m X| newtonrapsonsbypradeep.m X|+ Name trajectory.m toBinary.m saveee.m AThis file can be published to a formatted document. For more information, see the publishing yideo or help. 7-Efor 1-1:4 fprintf ('For %d eigen vector\n', i); 9disp'A eigen vector' 10- disp (A"X ( : , i)) 11- disp ( ' eigenvalue "X-' ) ; 12Vec (i)*x(:,i) 13-end thisCanEmpty.m testscores.dat test integration.m New to MATLAB? Watch this Video, see Examples or read GettingStarted For 3 eigen vector A*eigen vector 0.0529 0.5735 0.0187 -0.5360 yy.m (Script) Name ▲ Value 44 double 1.7643e-33:-24477e-. -2447eigenvalue*x- Min 44 double ns 37.9179:12.8690,-0.7..0 44 double 0.0529 0.5735 0.0187 f-0.5360 -0.816 O Type here to search ENG 1217 PM IN 03 04/19

b)

clc
clear all
close all
A=[2,3,1;-1,2,3;0,1,2];
disp('Characteristic polynomial is');
syms L
simplify(det(A-L*eye(3)))

MATLAB R2014a HOME PLOTS EDITOR Find Files Compare ▼ Comment Print new open Save Indent Breakpoints Run Run and Advance Advance Run and Find Time C: Users PRADEEP KALRA 、Documents MATLAB Current Folder Editor-CAUsersPRADEEP KALRA!Documents\MATLABAsaveee.m saveee.msecantbypradeep.m pradeep.m X | newtonrapsonsbypradeep.m X1+ Name ▼ trajectory.m toBinary.m This file can be published to a formatted document. For more information, see the publishing yideo or help. 1clc 3-close all thisCanEmpty.m 5disp ('Charactezistic polynomial is'): 6-syms L 7-simplify (det (A-L*eye (3) ) testscores.dat Command Window test integration.m New to MATLAB? Watch this Video, see Examples or read GettingStarted Characteristic polynomial is ns yy.m (Script) Name ▲ Value 2,3,1-1,2,3,0,1,2] x7 sym x7 sym S> Ln 7 Col 25 O Type here to search ENG 1219 PM IN 03 04/19

2)

clc
clear all
close all
A=[3,2,0;1,0,3;1,2,3];
[X,D]=eig(A);
disp('Eigen values are')
disp(diag(D));
disp('Eigen vectors are')
disp(X);

MATLAB R2014a HOME EDITOR Find Files Compare ▼ Comment Print New Open Save Breakpoints Run Run and Advance Advance Run and Indent Ele , i Find - Time C: Users PRADEEP KALRA 、Documents MATLAB Current Folder Editor-CAUsersPRADEEP KALRA!Documents\MATLABAsaveee.m saveee.msecantbypradeep.m pradeep.m newtonrapsonsbypradeep.m+ Name trajectory.m toBinary.m This file can be published to a formatted document. For more information, see the publishing yideo or help. 5[X, Di-eig (A) 6-disp( 'Eigen values are' 7-disp (diag (D)) thisCanEmpty.m diap ('Eigen vector disp (): s are') 10 Command Window New to MATLAB? Watch this Video, see Examples, or read Getting Started testscores.dat test integration.m Eigen values are 5.1172 2.3682 -1.4853 yy.m (Script) Eigen vectora are Name Value Min -0.4829 -0.8335 0.3883 0.2633 -0.8708 0.4857 0.3017 3,2,0:1,0,3:1,23] 5.1172,0,00,2.3682,01 -0.4829,-0.8335,0388.. -0.8 -0.7110 S> 2 usages of "D found Ln 9 Col7 O Type here to search ENG 12-20 PM US 03/04/19

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