#範例14-7：求四個『行向量』所生產行空間的基底
from sympy import *
# v1=(1,-2,0,3)
# v2=(2,-5,-3,6)
# v3=(0,1,3,0)
# v4=(2,-1,4,-7)
# v5=(5,-8,1,2)
M = Matrix([
    [1,2,0,2,5],
    [-2,-5,1,-1,-8],
    [0,-3,3,4,1],
    [3,6,0,-7,2]
    ])
M_simple = M.rref()
print('顯示高斯消去法簡化的梯形矩陣的echelon form =\n', M_simple)
M_rowspace = M.rowspace()
M_columnspace = M.columnspace()
print('輸出列空間的向量之線性組和= row space= \n', M_rowspace)
print('輸出行空間的向量之線性組和= column space= \n', M_columnspace)