# Ch-7-Prob-6-Old-이승진

## 2257 days ago by matrix

A=matrix(QQ,6,5,[1,2,0,2,5,-2,-5,1,-1,-8,0,-3,3,4,1,3,6,0,-7,2,0,0,0,0,2,0,0,0,-1,0]) print A.transpose().rref() print A.column_space() print A.rank()
 [ 1 0 0 -63/5 0 -6/5] [ 0 1 0 -39/5 0 -3/5] [ 0 0 1 13/5 0 1/5] [ 0 0 0 0 1 1/2] [ 0 0 0 0 0 0] Vector space of degree 6 and dimension 4 over Rational Field Basis matrix: [ 1 0 0 -63/5 0 -6/5] [ 0 1 0 -39/5 0 -3/5] [ 0 0 1 13/5 0 1/5] [ 0 0 0 0 1 1/2] 4 [ 1 0 0 -63/5 0 -6/5] [ 0 1 0 -39/5 0 -3/5] [ 0 0 1 13/5 0 1/5] [ 0 0 0 0 1 1/2] [ 0 0 0 0 0 0] Vector space of degree 6 and dimension 4 over Rational Field Basis matrix: [ 1 0 0 -63/5 0 -6/5] [ 0 1 0 -39/5 0 -3/5] [ 0 0 1 13/5 0 1/5] [ 0 0 0 0 1 1/2] 4