Let A be an n × n matrix, X be an n × 1 eigenvector of A, ? be an eigenvalue of A. Then AX = ?X This relationship can be demonstrated with the following code: Proc IML; A={ 1 0 1, 0 4 -1, 1 -1 2};...

Let A be an n × n matrix, X be an n × 1 eigenvector of A, ? be an eigenvalue of A. Then AX = ?X This relationship can be demonstrated with the following code: Proc IML; A={ 1 0 1, 0 4 -1, 1 -1 2}; RESET FUZZ; CALL EIGEN(eigval,eigvec,a); ax1=a*eigvec[,1]; ax2=a*eigvec[,2]; ax3=a*eigvec[,3]; lx1=eigval[1]*eigvec[,1]; lx2=eigval[2]*eigvec[,2]; lx3=eigval[3]*eigvec[,3]; PRINT a„eigval„eigvec„ax1 lx1„ax2 lx2„ax3 lx3; QUIT; Although the EIGEN call was used in the program, the EIGVAL and EIGVEC functions could also have been used