Linear Algebra Exam 2

subspace

A set S of vectors in V (S >= V) is a ________ of V if

1. for all x, y in S, x+y in S

2. for all x in S and all scalars a, ax in S

columns

every matrix vector product is a linear combination of the ______ of the matrix

span

the ____ of a set of vectors is the set of all possible lin. combs. of v1,…,vn

linearly independent

the vectors are ________ ________ if c1v1 +…+cnvn = 0 implies the coefficients = 0

dimension

the ________ of a v.s. V is the number of vectors in a basis for V