[理工] [線代] 98交大資訊

[mickeyha (M*schief)]

                        ┌       ┐
Suppose Q = [q1 q2 q3] =│1  1  1│
                        │1  1 -1│
                        │1 -1  1│
                        │1 -1 -1│
                        └       ┘

Let S12 = span(q1,q2) and S23 = span(q2,q3).
Whickh statements are true?

(a) The union of the two subspaces S12 and S23 forms a vector space.
(b) The intersection of the two subspaces S12 and S23 forms a vector space.
(c) The span(q1) is an orthogonal complement of the subspaces S23
(d) The rows of Q form a basis for the row space.
(e) The dim of the row space of Q is 3.

答案為 b e

小妹對a與b混淆了...甚至不太知道該怎麼定義"forms a vector space",

對c選項則是不清楚orthogonal complement的意思囧

如果有大大方便，可否解答一下，謝謝>___<




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◆ From: 1.162.97.237
※ 編輯: mickeyha        來自: 1.162.97.237         (01/21 23:06)
推 mqazz1:可以想一想黃子嘉x和y軸的例子 聯集和交集的差異
※ 編輯: mickeyha        來自: 1.162.97.237         (01/21 23:19)
推 Byzantin:a是聯集 b是交集 它問聯集(交集)後是否形成vector space
推 Byzantin:在vector space V中，S是V的子集 V裡面和所有S的vector
→ Byzantin:做內積等於0所形成的集合就是S的orthogonal complement