※ 引述《ruby791104 (阿年：）)》之銘言： : 1.Prove that any finite set of vectors that contains the zero vector muast be : linearly dependent. 請朝L.d的定義下手 : 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. (=>) av1+bv2=0 where a,b != 0 => av1=-bv2 (<=) If v2=kv1 where k !=0 then av1+bv2=av1+mv1=hv1=0 => v1 !=0 => h=0 => a=-m=-bk where a,b !=0 : 3.Prove that any nonempty subset of a linearly independent set of vectors : {v1,…,vn} is also linearly independent. L.i的子集還是L.i 用用看反證法吧 L.i的子集是L.d 挑選一組子集使得 av1+bv2+...+kvk=0 where a,b,..,k !=0 =>bv2+...+kvk=-av1 =>把-a除過去發現(a!=0)v1可由其他v組成 矛盾 Q.E.D : 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. 假設v1,..,vn已經是L.d + v 也是L.d (廢話) 假設v1,..,vn是L.i + v 變L.d 證明同3. : 5.Let v1, v2,..., vn be linearly independent vectors in a vector space V. : Show that v2,..., vn cannot span V. 老闆～ 反證法再來一次 大約就是 v1,..,vn span v1 <- V 但 v2,...,vn cannot span v1 Q.E.D : 以上，麻煩好心的大大們！（鞠躬 : PS：Merry Christmas！ 就將........ 沒人陪的耶誕夜 竟然是線代陪我 Q___Q 我也要是L.d了啦... -- 我絕對不會說 這是我的無名......... http://www.wretch.cc/blog/chris750630 --

※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 59.104.36.29 ※ 編輯: chris750630 來自: 59.104.36.29 (12/24 20:33)