Finding eigenvector with existing eigenvalues

I have a really simple example, which I would like to use for a better understanding of Eigenvector calculation in Matlab:
A = [3 6; 4 8]
x1 = [0.75; 1]
x2 = [-2; 1]
λ1 = 11
λ2 = 0
Which code do I have to use to have the simple output of x1 & x2?
I've tried several codes I found but always got a strange output:
CODE 1:
A = [4 1; 3 2];
[V,D] = eig(A);
V1 = V(:,1)
V2 = V(:,2)
OUTPUT 1:
v1 = [0.7071; 0.7071]
v2 = [-0.3162; 0.9487]
CODE 2:
A = [4 1; 3 2];
lambda=eig(A); % you should do it by solving det(A-lambda I)=0
V = ones(2);
for k=1:2
B = A-lambda(k)*eye(size(A));
% select pivot column
[~,j] = max(sum(B.^2,1));
othercolumn = 3-j;
V(j,k) = -B(:,j)\B(:,othercolumn);
end
% Optional: Make eigenvectors l2 norm = 1
V = V ./ sqrt(sum(V.^2,1))
OUTPUT 2:
V = [0.7071 -0.3162; 0.7071 0.9487]
May someone help me to get the mentioned outputs x1 = [0.75; 1] & x2 = [-2; 1]?
Thanks!!

2 comentarios

SALAH ALRABEEI
SALAH ALRABEEI el 12 de Jun. de 2021
you system is not linear indpendent, this means that is infinit eigenvectors. So ur x1 and x2 eig values, are just a case.
Oh I see, thanks!

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R2020b

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el 12 de Jun. de 2021

Comentada:

el 13 de Jun. de 2021

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