L ( W1 ⋃ W2 ) = W1 + W2 : Linear Algebra: Degree #L(W1⋃W2) #= #W1 #+ #W2 : #Linear #Algebra #: #Degree

Theorem :

    If W₁ and W₂ are any two subspace of a vector space V ( F ) then 

          L ( W₁ ⋃ W₂  ) = W₁ + W₂ .

Proof : 

       

* Linear combination of vectors

* linear sum of subspaces

* 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 

* 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

 * L ( S ) is a subspace of V.

#L(W1⋃W2) #= #W1 #+ #W2  : #Linear #Algebra #: #Degree             

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