VM270-8298

Honelako gehiago

exponential and logarithmic functions

by Maryam Alameri

Fun Ways to Learn

by Jef Fisher

Properties of Math

by Alfredo Villasana

Rules of Probability Distribution

by Maiya Farmer

VM270-8298

Chapter 1

Prop 1.9

V = U ⊕W if and only if V = U +W and U ∩W = {0}

Prop 1.8

(a) V = U1 + · · · + Un; (b) the only way to write 0 as a sum u1 + · · · + un, where each uj ∈ Uj , is by taking all the uj’s equal to 0.

Prop 1.7

U +W = {(x,y, 0) : x,y ∈ F}

Prop 1.6

v + (−1)v = 1v + (−1)v = 1 + (−1)v = 0v = 0

Prop 1.5

a0 = a(0 + 0) = a0 + a0

Prop 1.4

0v = (0 + 0)v = 0v + 0v

Prop 1.3

w=w+0=w+(v+w′)=(w+v)+w′ =0+w′ =w′

Prop 1.2

0′ = 0′ + 0 = 0