[理工] [線代] 基底與維度

[movo11 (Larry)]

(a)True or false:
                                     n
   (1)Let S be a nonempty subset of R  and V=span(S).

      If every vector in V can be uniquely expressed as

      a linear combination of vectors in S, then S is

      linearly independent.

   (2)A set S of vectors forms a basis for a subspace V
          n
      of R  if and only if the vectors of S are linearly

      linearly independent and the number of vectors equals

      the dimension of V.
(b)Suppose V is a vector space of dimension 7 and W a

   subspace of dimension 5.which one is(are) true?

   (1) Every basis for V can be reduced to a basis for W by

       removing 2 vectors.

   (2) Every basis of W can be extended to a basis for V by

       adding any 2 more vectors in V.

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◆ From: 1.174.135.168
推 ddczx:(a)1.T 2.F (b)(2)
→ Murasaki0110:(b.2)我覺得是F，如果加V中2個相依的vector
→ ddczx:也是,沒注意到any