RANK-NULLITY THEOREM : LINEAR ALGEBRA : B.SC.MATHEMATICS
For a video explanation, click here 👉 https://youtu.be/iazotp3QIsg * dim( V/W) = dimV-dimW * V/W forms a vector space. * Find the coordinates of 𝜶 = (4 ,5 ,6) w.r.t. x=(1,1,1),y = (-1,1,1),z = (1,0,-1) *dim ( W1 + W2 ) = dim ( W1 ) + dim ( W2) - dim ( W1 ⋂ W2 ) * If 𝜶 = ( 1 , -1 , 0 ) , 𝜷 = ( 2 , 1 , 3 ) find a basis for R3 containing 𝜶 and 𝜷 * Show that the set { ( 1 , 2 , 1 ) , ( 2 , 1 , 0 ) , ( 1 , -1 , 2 } forms a basis of V3 ( F ) * Theorem on Linear Dependence * linear sum of subspaces * What is a vector space * linear span of a set * L ( S ) = L ( S' ) * 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 ...