MATH136 Chapter Notes - Chapter 106-129: Coordinate Vector, Linear Independence, Additive Inverse

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Dan Wolczuk

Document Summary

If v is a vector space, then: 0~x = ~0 for all ~x v, ( ~x) = ( 1)~x for all ~x v. If s is a subset of v and s is a vector space under the same operations as v, then s is a called a subspace of v. ~vk} be a set of vectors in a vector space v. we de ne the span of b by. Spanb = {c1~v1 + + ck~vk|c1, . We say that the set spanb is spanned by b and that b is a spanning set for spanb. ~vk} is a set of vectors in a vectors space v, then spanb is a subspace of v. Let v be a vector space and ~v1, . , ~vk v. then, ~vi span {~v1, . , ~vk} in a vector space v is said to be linearly dependent if there exist coe cients c1, .