Linear Algebra Final Exam Study Guide

Subspace

A subset H of some vector space V such that H has these properties: (1) the zero vector of V is in H; (2) H is closed under vector addition; (3) H is closed under multiplication by scalars

Vector Space

a nonempty set of objects, called vectors, on which are defined two operations, called addition and multiplication by scalars (real numbers), subject to ten axioms

Linear Combination

any sum of scalar multiples of vectors

Zero Subspace

the set consisting of only the zero vector in a vector space V, which is a subspace of V, written as {0}