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 ...