Linear Combination of vectors : Linear Algebra : Degree #linear #combination #of #vectors



Linear Combination of vectors : 

                   Suppose 𝜶1, 𝜶2, … , 𝜶n   be any n  vectors in a vector space V ( F ) . Then for 

some scalars  the representation a1, a2, … , an  the representation  a1 𝜶1 +a2 𝜶2 +  … +an 

𝜶n is called a linear combination of vectors  𝜶1, 𝜶2, … , 𝜶n .


* linear sum of subspaces

* What is a vector space

* linear span of a set 

 * 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 

* Problem 2 on subspace of a vector space

 * Intersection of subspaces is again a subspace

  * union of subspaces of a vector space

  * Problems on linear combination




































































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

#linear #combination #of #vectors


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