How to use Linear Combinations
LINEAR COMBINATIONS Let V be a vector space over a field K . A vector v in V is a linear combination of vectors u ₁ + u ₂ + ⋯+ u ₙ in V if there exist scalars a ₁, a ₂ , ⋯, a ₙ in K such that v = a 1 u 1 + a ₂ u ₂ + ⋯+ a ₙ u ₙ Alternatively, v is a linear combination of vectors u ₁ + u ₂ + ⋯+ u ₙ if there is a solution to the vector equation v = x 1 u 1 + x ₂ u ₂ + ⋯+ x ₙ u ₙ whe...