devotion & mathematics

      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  ...

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    W 1  and  W 2  be any two subspaces of a vector spave V(F) then    W 1 ∩ W 2    is also             a subspace of V(F)  Proof :                                                       * What is a vector space  * Theorem on vector space      * Historical Introduction to Linear Algebra   * L...