cours algebre 2 s2

E E ×E−→ E
+
RER×E−→ E
.
RE+
.
(∀(x, y, z)∈E3)x+ (y+z) = (x+y) + z
(∀(x, y)∈E2)x+y=y+x
0E(∀x∈E)x+ 0E=x
(∀x∈E) (∃y∈E)x+y= 0 y y =−x
(∀x∈E) 1.x =x
(∀x∈E) (∀(α, β)∈R2)α.(β.x)=(α β).x
(∀x∈E) (∀(α, β)∈R2) (α+β).x =α.x +β.x
(∀(x, y)∈E2) (∀α∈R)α.(x+y) = α.x +α.y
R
R
R+
×
E=RnnRn
(x1, . . . , xn) (y1, . . . , yn) (x0
1, . . . , x0 n)
(x1, x2, . . . , xn)+(y1, y2, . . . , yn) = (x1+y1, x2+y2, . . . , xn+yn)