devotion & mathematics

For a video explanation, click here 👉 https://youtu.be/DTwC9rO2rWQ Theorem :               If  W 1 and   W 2 be two subspaces of the vector space V(F) . Then         1 )    W 1 + W 2   is a subspace of V(F)      and        2 )   W 1  ⊆    W 1 + W 2    and       W 2    ⊆  W 1 + W 2      Proof :                                        * Linear combination of vectors    *   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 b...

Linear Sum of Subspaces: Definition                                 Let   W 1 and   W 2 be two subspaces of the vector space V(F) . Then the linear sum  of the subspaces W 1 & W 2 , denoted by W 1 + W 2 , is the set of all sums 𝜶 1 + 𝜶 2 such  that   𝜶 1 𝞊 W 1 ,  𝜶 2 𝞊 W 2 i.e.  W 1 + W 2 = { 𝜶 1 + 𝜶 2 / 𝜶 1 𝞊 W 1 ,  𝜶 2 𝞊 W 2 }.   * LInear combination of vectors  * 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                                 ...