VM270-8298

Mere som dette

Miss Hannah's 1st Grade Class

af Hannah Cunningham

Whole Number Computation

af Whitney Steg

Elementary MathematicsmMAT156 FALL2012

af Laura Jaramillo

Fun Ways to Learn

af Jef Fisher

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