Problem 2 on subspace of a vector space : Linear Algebra : Degree #linear #algebra #degree #problem #subspace ##vector #space

For a video explanation ,click on 👉 https://youtu.be/JHbCJAh61eM
Problem 2 :

Let p,q,r be the fixed elements of a field F. Show that the set W of all triads (x,y,z) of elements of F, such that px+qy+rz = 0 is a vector 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

 * Problem 1 on subspace of a vector space 






























































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

#linear   #algebra #problem #on                      

      

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