9.wxmx

/ Check the diagonalizable property of matrices and find the corresponding eigenvalue and verify the Cayley- Hamilton theorem. /

load("eigen")$;

mat:entermatrix(4,4);

poly:expand(charpoly(mat,x));

Eigenvalues:eigenvalues(mat);

Eigenvectors:eivects(mat)[2];

P:determinant(addrow(matrix(Eigenvectors[1][1]),matrix(Eigenvectors[2][1]),matrix(Eigenvectors[2][2]),matrix(Eigenvectors[3][1])));

if P = 0 then("given matrix is not diagonalizable")

else ("given matrix is diagonalizable");