Union of subspaces of a vector space : Linear Algebra : Degree #union #subspace #linear #algebra

 

   

Theorem : 

               The union of subspaces of a vector space is again a subspace if and only if one is contained in the other.

  Proof : 

                               



 * 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




























































































#vector #algebra #vector algebra   #iit #jee #mains #dimension #basis #subspacec #linearalgebra      

 #union #subspace #linear #algebra                           



            

 

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