#範例14-6：求四個列向量所生產列空間的基底
from sympy import *
# v1=(1,-2,0,0,3)
# v2=(2,-5,-3,-2,6)
# v3=(0,5,15,10,0)
# v4=(2,6,18,8,6)
M = Matrix([
    [1,-2,0,0,3],
    [2,-5,-3,-2,6],
    [0,5,15,10,0],
    [2,6,18,8,6]
    ])
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)