# LA Chapter 8 Problem 4 solved by 김준현 revised by 이반석 finalized by Lee Naeul

## 2418 days ago by math2013

A = matrix([[3,-4],[-4,3]]) print A print print A.eigenvalues() E = identity_matrix(2) print print (A-7*E).echelon_form() print print (A-(-1)*E).echelon_form() x1 = vector([1,-1]) x2 = vector([1,1]) P = column_matrix([x1, x2]) print print P print print P^-1*A*P
 [ 3 -4] [-4 3] [7, -1] [4 4] [0 0] [ 4 -4] [ 0 0] [ 1 1] [-1 1] [ 7 0] [ 0 -1] [ 3 -4] [-4 3] [7, -1] [4 4] [0 0] [ 4 -4] [ 0 0] [ 1 1] [-1 1] [ 7 0] [ 0 -1]
B = matrix([[2,1,1],[1,2,1], [1,1,2]]) print B print print B.eigenvalues() E = identity_matrix(3) print print (B-4*E).echelon_form() print print (B-E).echelon_form() print print (B-E).echelon_form() x1 = vector([1,1,1]) x2 = vector([-1,1,0]) x3 = vector([-1,0,1]) P = column_matrix([x1, x2, x3]) print print P print print P^-1*B*P
 [2 1 1] [1 2 1] [1 1 2] [4, 1, 1] [ 1 1 -2] [ 0 3 -3] [ 0 0 0] [1 1 1] [0 0 0] [0 0 0] [1 1 1] [0 0 0] [0 0 0] [ 1 -1 -1] [ 1 1 0] [ 1 0 1] [4 0 0] [0 1 0] [0 0 1] [2 1 1] [1 2 1] [1 1 2] [4, 1, 1] [ 1 1 -2] [ 0 3 -3] [ 0 0 0] [1 1 1] [0 0 0] [0 0 0] [1 1 1] [0 0 0] [0 0 0] [ 1 -1 -1] [ 1 1 0] [ 1 0 1] [4 0 0] [0 1 0] [0 0 1]