(a) Decide whether the vectors (1,2,0,1), (2,-9,10,2), (1,1,2,-3), (2,0,4,-1) in R^4 are linearly independent.
(b) Let V be the subspace of R^4 spanned by
{ (2,1,4,0), (3,-1,2,1), (1,-7,-10,3) }.
Find a basis for V and write down its dimension.
vectors
2008-04-17 3:26 pm
回答 (1)
2008-04-17 11:57 pm
✔ 最佳答案
(a)圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Apr08/Crazymat3.jpg
So the system of linear equations has non-trivial solutions and hence the vectors are linear dependent.
(b) With implementation:
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Apr08/Crazymat4.jpg
So to speak, the 3 given vectors are linearly dependent and hence the basis for V can be reduced to:
V = a(2, 1, 4, 0) + b(3, -1, 2, 1) for all real a and b.
Hence , its dimension is 2.
參考: My Maths knowledge
收錄日期: 2021-04-15 01:25:22
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080417000051KK00365