[理工] 線代

[KAINTS (RUKAWA)]

1.It's possible for different bases for a paticular
  subspce to contain different numbers of vectors.

(F):可我假設一組基底為(1,2,3) 另一組為(4,8,12)
這樣不就有different numbers of vectors?


                                                     n
2.The matrix representation of a linear operator on R
                             n
with respect to a basis for R  is an n*n matrix.

(T):why?


3.The B-coordinate vector of a vextor in B is a standard vector.

(T):why?


4.The columns of any matrix form a basis for its
  column space.

(F):只有row space 有這個性質嗎?還是?



5.The row space of an m*n matrix A is the set
               n
  {Av:v is in R }.

(F):why?

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◆ From: 42.64.65.211
推 Rain0224:第一題對原文有誤解，原文問的是基底的數量，而非基底向
→ Rain0224:量各項的數字
→ ddczx:第一題應該是指基底內元素的數量吧
推 ddczx:第四題應該是因為基底必須線性獨立但行與行之間可能相依
→ Rain0224:第二題，在R^n空間上進行轉換，矩陣表示法若不是n*n，就
→ Rain0224:得不到R^n上的向量
→ Rain0224:第五題，{Av:v is in R^n }是column space
推 ILzi:第三題 B-coordinate vector：以某向量在B基底的表示法
→ ILzi:B基底的某向量在B基底的表示法當然是基本向量(ei)