Ch-6-Prob-9-New-이승진

1893 days ago by matrix

A=matrix(QQ, 3, 5, [1, 1, 1, 4, 4, 2, 3, 4, 9, 16, -2, 0, 3, -7, 11]) print A.rref() print A.right_kernel() # The solution space of the system of linear equations Ax=0 print A.right_nullity() 
        
[ 1  0  0  2 -1]
[ 0  1  0  3  2]
[ 0  0  1 -1  3]
Vector space of degree 5 and dimension 2 over Rational Field
Basis matrix:
[    1     0 -11/7  -2/7   3/7]
[    0     1   5/7  -1/7  -2/7]
2
[ 1  0  0  2 -1]
[ 0  1  0  3  2]
[ 0  0  1 -1  3]
Vector space of degree 5 and dimension 2 over Rational Field
Basis matrix:
[    1     0 -11/7  -2/7   3/7]
[    0     1   5/7  -1/7  -2/7]
2
A=matrix(QQ, 3, 5, [1, 1, 1, 4, 4, 2, 3, 4, 9, 16, -2, 0, 3, -7, 11]) w=vector([1,2,-3]) print A.augment(w).rref() 
        
[ 1  0  0  2 -1  0]
[ 0  1  0  3  2  2]
[ 0  0  1 -1  3 -1]
[ 1  0  0  2 -1  0]
[ 0  1  0  3  2  2]
[ 0  0  1 -1  3 -1]