devotion & mathematics

For a video explanation, click the link 👉 https://youtu.be/Rtwx1-VKBQo Theorem :                    A non-empty set W is a subset  of a vector space V(F)  . W is a subspace of V                  if and only if a 𝞊 F and 𝝰 , 𝞫 𝞊 W ⇒ a𝝰 + 𝞫 𝞊 W .  Proof:            *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 ...

For a video explanation , click the link 👉 https://youtu.be/jfKdIWXVYsQ Theorem :             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 proof :      *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...

  For a video explanation , click the link 👉 https://youtu.be/xxeVZKw8MAc Theorem :             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.  Proof :             *Linear Sum of Subspaces * External Composition   * 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 is  𝜶 𝞊 W, 𝞫 𝞊 W ⇒  a𝜶 +b𝞫 𝞊 W # Let V(F) be...

For a video explanation , click the link 👉 https://youtu.be/ukbd5oWXMH4                        Vector Subspace : Definition         Let V(F) be a vector space and W ⊆ V. Then W is said to be a subspace of V if W             is    itself a  vector space over F with the same operation of vector addition and                  scalar   multiplication in V.  Example :          * The set of 2x2 triangular matrices is a vector subsapce of the space of all 2x2            with   matrices  with real entries.  *Linear Sum of Subspaces * External Composition     * What is a vector space  * Theorem on vector space      * Historical Introduction to Linear Algebra *   Let V(F) be a vector space and let...