Please I need your help.

I need to prove or disprove the following.

a_1 a_2 real numbers.

x, y both in R^3.

A is a convex set in R^3.

a.x in a.A and b.y in b.A. Then ax + by is in (a+b)A

(a.A, b.A, (a+b)A are all Homothetic transformations)

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- Apr 30th 2013, 09:04 PMkezmanHomothetic property
Please I need your help.

I need to prove or disprove the following.

a_1 a_2 real numbers.

x, y both in R^3.

A is a convex set in R^3.

a.x in a.A and b.y in b.A. Then ax + by is in (a+b)A

(a.A, b.A, (a+b)A are all Homothetic transformations) - Apr 30th 2013, 10:28 PMGusbobRe: Homothetic property
Consider the unit vectors $\displaystyle v_1=(1,0,0)$ and $\displaystyle v_2=(0,1,0)$ and the set $\displaystyle A=\{a\cdot v_1|a\in \mathbb{R}\}\cup \{b\cdot v_2|2\in \mathbb{R}\}$

- Apr 30th 2013, 11:56 PMkezmanRe: Homothetic property
Im sorry I forgot that A is a convex set