# Shared Flashcard Set

## Details

Linear Algebra test 2
material from 4.1
34
Mathematics
10/24/2016

Term
 vector in a plane
Definition
 geometrically represented by a directed lign segment with its initial point at the origin and its terminal point at (x1,x2)
Term
 ordered pair (x1,x2)
Definition
 how we represent the vector x. Also x1 and x2 are called the components of the vector x.
Term
 equal vector
Definition
 we say two vectors x=(x1,x2) and u=(u1,u2) are equal if and only if x1=u1 and x2=u2
Term
Definition
 the sum of two vectors x=(x1,x2) and u=(u1,u2) is defined as the vector x+u=(x1+u1, x2+u2)
Term
 vector scalar multiplication
Definition
 to multiply a vector x=(x1,x2) by a scalar c we multiply each component by c. c1*x=(cx1,cx2)
Term
 vector subtraction
Definition
 as a consequence of vector addition and scalar multiplication, we can now define the subtraction of two vectors x=(x1,x2) and u=(u1,u2) as x+(-u)=x-u=(x1-u1, x2-u2)
Term
 negative of vector x
Definition
 (-1)x=-x
Term
 u+v is a vector in the plane
Definition
Term
 u+v=v+u
Definition
Term
 (u+v)+w=u+(v+w)
Definition
Term
 u+0=0
Definition
Term
 cu is a vector in the plane
Definition
 closure under scalar multiplication
Term
 c(u+v)=cu+vu
Definition
 distributive property
Term
 (c+d)u=cu+du
Definition
 distributive property
Term
 c(du)=(cd)u
Definition
 associative property of multiplication
Term
 1(u)=u
Definition
 multiplicative identity property
Term
 Rn
Definition
 vector operations extended to higher dimensions
Term
 ordered n-tuple
Definition
 represents a vector in n-space and has the form (x1,x2,x3,...xn). We can either view these n-tuples as points in Rnwith the xi's as its coordinates or as a vector x=(x1,x2,...xn) with xi's as its components
Term
 two vectors are equal...
Definition
 if and only if their components are equal
Term
 standard operations in Rn
Definition
 let u=(x1,x2...,un) and v=(v1,v2,...vn) be vectors in Rn and c be a real number. Then the sum of u and v is defined as the vector u+v=(u1+v1,u2+v2,...un+vn) and the scalar multiple of u by c is defined as the vector cu=(cu1,cu2,...cun)
Term
 the negative of vector u in Rn
Definition
 -u=(-u1,-u2,...-un)
Term
 difference between two vectors u and v
Definition
 u-v=(u1-v1,u2-v2,...un-vn)
Term
 u+v is a vector in Rn
Definition
Term
 u+v=v+u
Definition
Term
 (u+v)+w=u+(v+w)
Definition
Term
 u+0=u
Definition
Term
 u+(-u)=0
Definition
Term
 cu is a vectory in R
Definition
 closure under scalar multiplication
Term
 c(u+v)=cu+vu
Definition
 distributive property
Term
 (c+d)u=cu+cd
Definition
 distributive property
Term
 c(du)+(cd)u
Definition
 associative property of multiplication
Term
 1(u)=u
Definition
 multiplicative identity property
Term