MATH136 Chapter Notes - Chapter 1-40: Anticommutativity, Triangle Inequality, Distributive Property

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

Document Summary

Let ~x = x1 xn and ~y = y1 yn be two vectors in rn. ~x + ~y = x1 + y1 xn + yn and scalar multiplication by a real number c (called a scalar) by c~x = cx1 cxn. , ck r we call the sum c1~v1 + + ck~vk a linear combination of ~v1, . 1: c(~x + ~y) = c~x + c~y, 1~x = ~x. ~vk} be a set of vectors in rn. 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. There exists some vector ~vi, 1 i k such that ~vi can be written as a linear combination of ~v1, . , ~vk} in rn is said to be linearly dependent if there exist coe cients c1, . , ~vk} is said to be linearly independent if the only solution to.