(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

α ((0, y1) + (0, y2)) = α(0, y1 + y2) = (0, α(y1 + y2))
= (0, αy1) + (0, αy2) = α(0, y1) + α(0, y2)
α (β(0, y)) = α(0, βy) = (0, αβy) = αβ(0, y)
1(0, y) = (0, 1y) = (0, y)
= (x, y) ∈ IR 2 | y = mx = {(x, mx) | x ∈ IR} ¡
2
IR
Rm
£¢ G ¡ (IR 2 , +, ·)
(x, mx) + (y, my) = (x + y, mx + my) = (x + y, m(x + y))
= (y + x, m(y + x)) = (y + x, my + mx)
= (y, my) + (x, mx)
(x, mx) + ((y, my) + (z, mz)) = (x, mx) + (y + z, my + mz)
= (x, mx) + (y + z, m(y + z))
= (x + (y + z), mx + m(y + z))
= ((x + y) + z, m(x + y) + mz)
= (x + y, m(x + y)) + (z, mz)
= ((x, mx) + (y, my)) + (z, mz)
(x, mx) + (e, me) = (x, mx) =⇒ (e, me) = 0)
(0,
(x, mx) + (−x, −mx) = (0, 0) =⇒ (−x, −mx) = −(x,
mx)
(x, mx)
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