New-WinRAR-ZIP-archive.zip_R and MATLAB_reduced row echelon_row

function eigen2(A) % eigen2 Characteristic polynomial, eigenvalues, eigenvectors % of a 2 by 2 matrix. % % eigen2(A) prints the characteristic polynomial det(A-e*I), % eigenvalues, and eigenvectors of A. % % If A is not diagonalizable, its single eigenvector is % printed twice. d = A(1,1)*A(2,2) - A(1,2)*A(2,1); t = A(1,1) + A(2,2); e1 = (t + sqrt(t^2 - 4*d))/2; e2 = (t - sqrt(t^2 - 4*d))/2; if A(1,2) ~= 0 x1 = [A(1,2); e1-A(1,1)]; x2 = [A(1,2); e2-A(1,1)]; elseif A(2,1) ~= 0 x1 = [e1-A(2,2); A(2,1)]; x2 = [e2-A(2,2); A(2,1)]; else x1 = [1; 0]; x2 = [0; 1]; end disp(' ') disp('For this matrix, the polynomial whose roots are the eigenvalues is:') disp([' e^2 - ' num2str(t) '*e + ' num2str(d) ' = 0']) disp(' ') disp('The first eigenvalue and eigenvector are:') e1 x1 disp(' ') disp('The second eigenvalue and eigenvector are:') e2 x2