devotion & mathematics

  Problems on linear combination :  Problem 1 :                   Express the vector 𝜶 = (1 , -2 , 5 ) as a linear combination of the vectors e 1 = ( 1 , 1 , 1 ) , e 2 = ( 1 , 2 , 3 ) , e 3 = ( 2 , -1 , 1 ). Solution : Problem 2 : Show that the vector 𝜶 = ( 2 , -5 , 3 ) in R 3 can not be expressed as a linear combination of the vectors e 1 = ( 1 , -3 , 2 ) ; e 2 = ( 2 , -4 , -1 ) ; e 3 = ( 1 , -5 , 7 ) Solution : * 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           ...

Linear Combination of vectors :                      Suppose  𝜶 1 , 𝜶 2 , … , 𝜶 n   be any n  vectors in a vector space V ( F ) . Then for  some scalars   the representation  a 1 , a 2 , … , a n   the representation    a 1 𝜶 1 +a 2 𝜶 2 +   … +a n   𝜶 n  is  called a linear  combination of vectors    𝜶 1 , 𝜶 2 , … , 𝜶 n . * 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                                     ...