Get the unique solution to a simultaneous equation

I wish to find the eigenvalues and vectors of a matrix without the big function

clc
clear all
close all
syms lamda x1 x2
A = input('Enter the matrix: ');
n = size(A);
if n(1) == n(2)
  disp(['Characterisitc equation = ',char(det(A-lamda*eye(size(A)))),' = 0']);
  disp('Eigen Values: ');
  eigen_values = solve(det(A-lamda*eye(size(A))),lamda);
  for i =1:size(A)
      disp(['Vector ',num2str(i)]);
      mat = eigen_values(i).*eye(size(A));
      X = linsolve(A-mat,zeros(n(1),1))
  end
else
 disp('The matrix dimensions do not match');
end

I am able to find the Eigen values but the Eigen vector comes out [0;0]. How do I set a condition to obtain unique/distinct values.