[理工] [線代]-線性獨立／依賴五題證明題
1.Prove that any finite set of vectors that contains the zero vector muast be
linearly dependent.
2.Let v1, v2 be two vectors in a vector space V. Show that v1 and v2 are
linearly dependent if and only if one of the vectors is a scalar multiple of
the other.
3.Prove that any nonempty subset of a linearly independent set of vectors
{v1,…,vn} is also linearly independent.
4.Let {v1,…,vn} be a spanning set for the vector space V, and let v be any
other vector in V. Show that v, v1,..., vn are linearly dependent.
5.Let v1, v2,..., vn be linearly independent vectors in a vector space V.
Show that v2,..., vn cannot span V.
以上，麻煩好心的大大們！（鞠躬
PS：Merry Christmas！
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 120.127.32.231
推
12/24 19:35, , 1F
12/24 19:35, 1F
推
12/24 20:04, , 2F
12/24 20:04, 2F
討論串 (同標題文章)
以下文章回應了本文：
完整討論串 (本文為第 1 之 2 篇)：