Theorem on vector space : Linear Algebra : Degree

For a video explanation , click the link  https://youtu.be/YB_p6iPSIfQ
  Theorem : 

           Let V(F) be a vector space and 0 and  O be the zero scalar and zero vector respectively. Then

   (i)  a O = O ∀ a 𝞊 F.

  (ii) o 𝜶 = O ∀ a 𝞊 F, 𝜶 𝞊 V  

  (iii) a ( - 𝜶 ) = - (a𝜶) = (-a) 𝜶 ∀ a 𝞊 F , 𝜶 𝞊 V

  (iv) a ( 𝜶 - 𝛃 ) = a𝜶 - a𝛃 ∀ a 𝞊 F , 𝜶,𝛃 𝞊 V. 

  Proof : 

                         


* Historical Introduction to Linear Algebra

 * What is a vector space


































































































#vector #algebra #vector algebra   #iit #jee #mains #dimension #basis  #theorem #on #vector #space #unit1 #unit #1                           

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