Bigbook+Chapter6+Problem9+solved+by+박시현

2077 days ago by darkextra

(1) 영공간의 차원 찾기

A = matrix(QQ, 4, 6, [2,5,-3,7,1,3, 5,-2,9,8,4,-2, -4,3,8,11,-5,2, 11,0,-2,4,10,-1]) print A.echelon_form() print A.rank() print A.right_nullity() 
       
[       1        0        0  264/487  434/487  -47/487]
[       0        1        0  863/487 -105/487  302/487]
[       0        0        1  478/487  -48/487  -15/487]
[       0        0        0        0        0        0]
3
3
[       1        0        0  264/487  434/487  -47/487]
[       0        1        0  863/487 -105/487  302/487]
[       0        0        1  478/487  -48/487  -15/487]
[       0        0        0        0        0        0]
3
3

따라서 영공간의 차원은 Rank-nullity 정리에 의해 3이 된다.

 

(2) 행렬 A의 선형변환 행렬 찾기