Necessary Condition 1 for subspace : LInear Algebra

 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 : 

          


* 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 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 #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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