Ch-7-Prob-7-Solved-황성빈

1861 days ago by matrix

A=matrix(QQ, 5, 8, [1,2,0,1,0,3,0,6,0,4,-1,2,4,2,6,6,0,0,3,4,5,1,5,6,0,-1,2,4,5,6,3,0,1,3,4,3,6,7,2,1]) A.echelon_form() 
       
[      1       0       0       0       0    41/4 -127/25 -157/20]
[      0       1       0       0       0    -5/2   38/25   39/10]
[      0       0       1       0       0    -5/2   12/25   21/10]
[      0       0       0       1       0    -9/4   51/25  121/20]
[      0       0       0       0       1     7/2  -23/25  -49/10]
[      1       0       0       0       0    41/4 -127/25 -157/20]
[      0       1       0       0       0    -5/2   38/25   39/10]
[      0       0       1       0       0    -5/2   12/25   21/10]
[      0       0       0       1       0    -9/4   51/25  121/20]
[      0       0       0       0       1     7/2  -23/25  -49/10]
A=matrix(QQ, 5, 8, [1,2,0,1,0,3,0,6,0,4,-1,2,4,2,6,6,0,0,3,4,5,1,5,6,0,-1,2,4,5,6,3,0,1,3,4,3,6,7,2,1]) print 'nullity(A)=' A.right_nullity() 
       
nullity(A)=
3
nullity(A)=
3
A=matrix(QQ, 5, 8, [1,2,0,1,0,3,0,6,0,4,-1,2,4,2,6,6,0,0,3,4,5,1,5,6,0,-1,2,4,5,6,3,0,1,3,4,3,6,7,2,1]) print 'rank(A) = n- nullity(A) = 8 - nullity(A)' print 'rank(A)=' A.rank() 
       
rank(A) = n- nullity(A) = 8 - nullity(A)
rank(A)=
5
rank(A) = n- nullity(A) = 8 - nullity(A)
rank(A)=
5