# ch8 problem5 by 김도형

## 562 days ago by g1.kjiwon

A = matrix(QQ,[[3,0,1],[4,-2,8],[-4,0,-1]]) print A print print A.eigenvalues() E = identity_matrix(3) print print (-2*E-A).echelon_form() print print (E-A).echelon_form() print print A.right_eigenvectors() print print A.is_diagonalizable()
 [ 3 0 1] [ 4 -2 8] [-4 0 -1] [-2, 1, 1] [1 0 0] [0 0 1] [0 0 0] [ 1 0 1/2] [ 0 1 -2] [ 0 0 0] [(-2, [ (0, 1, 0) ], 1), (1, [ (1, -4, -2) ], 2)] False [ 3 0 1] [ 4 -2 8] [-4 0 -1] [-2, 1, 1] [1 0 0] [0 0 1] [0 0 0] [ 1 0 1/2] [ 0 1 -2] [ 0 0 0] [(-2, [ (0, 1, 0) ], 1), (1, [ (1, -4, -2) ], 2)] False

 Traceback (click to the left of this block for traceback) ... SyntaxError: invalid syntax Traceback (most recent call last): File "", line 1, in File "_sage_input_11.py", line 10, in exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyICdhLGIsYyxkLGUsZixnLGgsaScKUCA9IG1hdHJpeChbWydhJywnYicsJ2MnXSxbJ2QnLCdlJywnZiddLFsnZycsJ2gnLCdpJ11dKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in File "/tmp/tmpj6F1jl/___code___.py", line 2 var 'a,b,c,d,e,f,g,h,i' ^ SyntaxError: invalid syntax