problem 1 on subspace of a vector space: linear algebra : Degree

For a video explanation, click the link 👉 https://youtu.be/FdPspiSjc-c

          

Problem :

         The set W of ordered triads ( x , y , 0 ) where x , y 𝞊 F  is a subspace of   V₃(F).

Solution :  

            

                     

 * 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. The necessary and sufficient conditions for W 

    to be a subspace of V is  𝜶 𝞊 W, 𝞫 𝞊 W ⇒  a𝜶 +b𝞫 𝞊 W

#The #set #W #of #ordered #triads #( x , y , 0 ) #where #x #, #y #𝞊 #F  #is #a #subspace #of   #V₃(F) #.

#ThesetWoforderedtriads(x,y,0)wherex,y𝞊FisasubspaceofV₃(F).

#vector #algebra #vector algebra   #iit #jee #mains #dimension #basis #subspacec #linearalgebra  #problem #example