# 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