Vector Subspace : Linear Algebra #vector #sub #space #linear#algebra

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 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.






















































































































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

 #vector #space #linear#algebra #subspace  #sub                    


















                                   

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