(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H
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F1 = {(2a2, a2, −a2) | a2 ∈ IR}<br />
¨¥ ¨ F1<br />
¢ <br />
<br />
<br />
(2x, x, −x) + (2y, y, −y) = (2x + 2y, x + y, −x − y)<br />
<br />
= (2y + 2x, y + x, −y − x)<br />
= (2y, y, −y) + (2x, x, −x)<br />
(2x, x, −x) + ((2y, y, −y) + (2z, z, −z))<br />
= (2x, x, −x) + (2y + 2z, y + z, −y − z)<br />
= (2x + 2y + 2z, x + y + z, −x − y − z)<br />
= (2x + 2y, x + y, −x − y) + (2z, z, −z)<br />
= ((2x, x, −x) + (2y, y, −y)) + (2z, z, −z)<br />
<br />
(2x, x, −x) + (2e, e, −e) = (2x, x, −x) =⇒ (2e, e, −e) = (0, 0, 0)<br />
<br />
<br />
(2x, x, −x) + (−2x, −x, x) = (0, 0, 0) =⇒ − (2x, x, <br />
−x)<br />
(2x, x, −x)<br />
(F1, +) ¡ ¢ ¢ ¥¤ <br />
<br />
<br />
α ((2x, x, −x) + (2y, y, −y)) = α (2x + 2y, x + y, −x − y)<br />
= (2αx + 2αy, αx + αy, −αx − αy)<br />
= (2αx, αx, −αx) + (2αy, αy, −αy)<br />
= α (2x, x, −x) + α (2y, y, −y)<br />
α (β (2x + 2y, x + y, −x − y)) = αβ (2x + 2y, x + y, −x − y)<br />
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