# LA.Ch8.Ex1.NEW.SC.Kim

## 2413 days ago by seongchan

x1, x2, x3, x4 = var('x1, x2, x3, x4') f(x1, x2, x3, x4) = [x1-x2, x3-2*x2, x3+3*x4, x4-4*x1] T = linear_transformation(QQ^4, QQ^4, f) v1=vector([1, 0, 2, -1]) v2=vector([1, 1, -4, 0]) v3=vector([0, -1, 2, 3]) v4=vector([-2, 4, 1, 3]) A=column_matrix([v1, v2, v3, v4, T(v1), T(v2), T(v3), T(v4)]) print A print B=A.echelon_form() print B print C=B.submatrix(0, 4, 4, 4) print C
 [ 1 1 0 -2 1 0 1 -6] [ 0 1 -1 4 2 -6 4 -7] [ 2 -4 2 1 -1 -4 11 10] [-1 0 3 3 -5 -4 3 11] [ 1 0 0 0 115/104 -113/52 381/104 -47/13] [ 0 1 0 0 1/8 -3/4 -1/8 -3] [ 0 0 1 0 -147/104 -31/52 99/104 36/13] [ 0 0 0 1 3/26 -19/13 33/26 -4/13] [ 115/104 -113/52 381/104 -47/13] [ 1/8 -3/4 -1/8 -3] [-147/104 -31/52 99/104 36/13] [ 3/26 -19/13 33/26 -4/13] [ 1 1 0 -2 1 0 1 -6] [ 0 1 -1 4 2 -6 4 -7] [ 2 -4 2 1 -1 -4 11 10] [-1 0 3 3 -5 -4 3 11] [ 1 0 0 0 115/104 -113/52 381/104 -47/13] [ 0 1 0 0 1/8 -3/4 -1/8 -3] [ 0 0 1 0 -147/104 -31/52 99/104 36/13] [ 0 0 0 1 3/26 -19/13 33/26 -4/13] [ 115/104 -113/52 381/104 -47/13] [ 1/8 -3/4 -1/8 -3] [-147/104 -31/52 99/104 36/13] [ 3/26 -19/13 33/26 -4/13]