VM270-8298

Mer som dette

First Mind Map

Ved J.J. Brunmeier

Miss Hannah's 1st Grade Class

Ved Hannah Cunningham

Polynomial Equations and Inequalities

Ved Fuad Jahen

Linear Algebra Final

Ved Chang Yeh-Yung

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