Show all work Project4m is also in the picture trix A2 1 21

trix A---2 1 21 . Print out the M of the ma ut it ? nt out the Matlab outp Question 6: Run the provided program \"projec Find the d to obtain the randomly generated matrix [131 A0x10 and a randomly generated initial vector vector zo. Find the dominant eigenvalue and a corre- .m sponding eigenvector of A using the Power Me le when mari- rations m Is safer to p the eigenve ange between thently close, for example, when mar(abs(4m ze) CU001 if there when +change between the enhut it may- ag the Power Method Version 11. Decide when to stop your iteration +1 and zk entries). Note: The first few iterations may look like that are sufficiently cl form more iterations (210) to obtain the domian ector is con vergent but it may lead to a wrong eigenval o obtain the dominant eigenvalue and the corresponding ue. It is safer to per- eigenvector.

Solution

n=10;

rand(\'state\',sum(100*clock));

m=int8(n*rand(1));

rand(\'state\',sum(100*clock));

v=rand(n,1);

I=eye(n);

v=v+1.5*I(:,m)

D=diag(v);

while 0<1

rand(\'state\',sum(100*clock));

P=rand(n);

if (abs(det(P))>0.01) break;

end

end

A=P*D*inv(P)

rand(\'state\',sum(100*clock));

x0=rand(n,1)

%Solution for dominant eigen value

x=x0;

for i=1:15

c=transpose(x)*x;

D=(1/sqrt(c))*x;

x=A*D;

end

c=transpose(x)*x;

Dominant_eigenvalue=sqrt(c)

[V,D]=eig(A)

%The last column vector in V represents the eigen vector for dominant eigen value