(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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74 CAPÍTULO 7. £¡ §© ¢¦£ ¤ ¢¥ § ¡<br />
¡ § ⊕ +<br />
<br />
IR<br />
(x, y) ∈ IR 2 <br />
(x, y) ⊕ (e1, e2) = (x, y)<br />
⊕ ©<br />
¢¡<br />
(x + e1, y + e2) = (x, y) ⇐⇒<br />
(e1, e2) ∈ IR 2 <br />
x + e1 = x<br />
y + e2 = y<br />
⇐⇒<br />
<br />
e1 = 0<br />
e2 = 0<br />
(e1, e2) = (0, 0) ¡ IR 2 ⊕<br />
<br />
©<br />
⊕ (x, y) ∈ IR 2 <br />
(x, y) ∈ IR 2 <br />
¢¡<br />
(x + x, y + y) = (0, 0) ⇐⇒<br />
(x, y) ⊕ (x, y) = (0, 0)<br />
x + x = 0<br />
y + y = 0<br />
⇐⇒<br />
x = −x<br />
y = −y<br />
(−x, −y) = − (x, ¡ y) (x, <br />
y) ¢<br />
<br />
<br />
2 <br />
IR<br />
¡ ¢ 2<br />
, ⊕ IR ,<br />
¡<br />
⊕, ¨§ ⊙ ⊕<br />
<br />
α IR ∈<br />
α ⊙ ((x1, y1) ⊕ (x2, y2)) = α ⊙ (x1 + x2, y1 + y2)<br />
(x1, y1), (x2, y2) ∈ IR 2 <br />
= (α(x1 + x2), α(y1 + y2))<br />
= (α x1 + α x2, α y1 + α y2)<br />
<br />
(α ⊙ (x1, y1)) ⊕ (α ⊙ (x2, y2)) = (α x1, α y1) ⊕ (α x2, α y2)<br />
= (α x1 + α x2, α y1 + α y2)<br />
α ⊙ ((x1, y1) ⊕ (x2, y2)) = (α ⊙ (x1, y1)) ⊕ (α ⊙ (x2, y2))