CHAPTER I: LINEAR ALGEBRA - OCW UPM

AFFINE AND PROJECTIVE GEOMETRY, E. Rosado & S.L. Rueda
Let V be a real vector space.
A vector u ∈ V is a linear combination of the vectors u 1 , . . . , u n ∈ V if there
exist scalars a 1 , . . . , a n ∈ R such that
n∑
u = a 1 u 1 + . . . + a n u n = a i u i .
Let C be a nonempty subset of V . Then the set of all the linear combinatuions
with vectors of C,
n∑
〈C〉 = { a i u i | a i ∈ R, u i ∈ C}
i=1
is a vector subspace of V which is called the subspace generated by C.
Let C = {(1, 0, 0), (0, 1, 1)} ⊆ R 3 . Then
〈C〉 = {(a, b, b) | a, b ∈ R}.
i=1