L(S) is a subspace : Linear Algebra : Degree #L(S) #is #a #subspace #Linear #Algebra #: #Degree

Theorem : 

      For any subset S of a vector space V( F ) , the linear span of S L ( S ) is a subspace of V. 

Proof :             

            

* Linear combination of vectors

* linear sum of subspaces

* What is a vector space

 * Theorem on vector space  

 * Historical Introduction to Linear Algebra

 * Let V(F) be a vector space and let W ⊆ V. The necessary and sufficient conditions for W 

            to be a subspace of V are (i) 𝜶 𝞊 W, 𝞫 𝞊 W ⇒  𝜶 - 𝞫 𝞊 W

                                                     (ii) a 𝞊 F , 𝜶 𝞊 W ⇒ a𝜶 𝞊 W.

* Let V(F) be a vector space and let W ⊆ V. The necessary and sufficient conditions for W 

    to be a subspace of V is  𝜶 𝞊 W, 𝞫 𝞊 W ⇒  a𝜶 +b𝞫 𝞊 W

 * Problem 1 on subspace of a vector space 

* Problem 2 on subspace of a vector space

 * Intersection of subspaces is again a subspace

  * union of subspaces of a vector space

 * Problems on linear combination

 *  L ( W₁ ⋃ W₂  ) = W₁ + W₂ 

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 #L(S) #is #a #subspace  #Linear #Algebra #: #Degree