Intersection of subspaces of a vector space : Linear Algebra : Degree

For a video explanation, click the link 👉 https://youtu.be/Ai7fvMYv4Jo

Theorem : 

          The intersection of subspaces of  a vector space is again a subspace of the vector                space

                                          Or

         If   W1 and W2 be any two subspaces of a vector spave V(F) then   W1∩W2   is also             a subspace of V(F)

 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

 * union of subspaces of a vector space







































































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

intersection #vector #space                          


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