Algebra lineal

1. Demuestre que Ѵ es un espacio vectorial
1.- V=
Vectores Escalares
u=
v= β = -3
w=

1.-u + v εѴ
+ =
2. u + v = v + u
= +
=
3. (u + v) + w = u + (v + w)

+ = +
= +

4. u + 0 = 0 + u = u
+ = +

5. u + (-u) = 0+ =
=
6. α u = εѴ

7. α ( u + v ) = αu + αv

= +

8. ( α + β ) u = αu + βu
(2+ -3) = +
(-1) = +
=
9.- α (βu) = (α β)u

=
10.- 1u = uSi es un espacio vectorial

2.-

Suma definida por:
(x1 , y1) + (x2 , y2) = (x1* x2 , y1* y2)
Multiplicación por escalar ordinaria

VectoresEscalares
u =(-1 , 3) α=2
ν = (4 , 0) β= 3
w =(1, 2)

1.- u + v εѴ2. u + v = v + u



3. (u + v) + w = u + (v + w)No es un espacio vectorial
4. u + 0 = 0 + u = u



3.
Suma ordinaria
Multiplicación x escalar definidapor: c (x,y) = (3 cx, 0)

Vectores Escalares
u= (2, 1) α = 2
v= ( 1 ,3) β = -3
ω=(0 , -4)

1.- u + v εѴ2. u + v = v + u
(2 , 1) + (1 , 3) (3 , 4 ) = (1 , 3) + (2 , 1)
(3 , 4) (3 , 4) = (3 , 4)

3. (u + v) + w = u + (v + w)
(3 ,4) + (0, -4) = (2 , 1) +
(3 , 0) = (2 , 1) + (1, -1)
(3 , 0) = (3 , 0)
4. u + 0 = 0 + u = u

(2 , 1) + (0 , 0) = (0 , 0) + (2 , 1) = (2 , 1)
(2 , 1) = (2 , 1) = (2 , 1)

5. u + (-u) = 0...