I need help with this problem that I don't know how to solve.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

For each positive integer m, it's defined a subset of R2 as Wm={(mx,x)|x in R}

(a) Prove that each Wm is a subspace of R2.

(b) ¿Is the union of all Wm a subspace of R2?. Prove it.

2. Relevant equations

None.

3. The attempt at a solution

Trying to prove (a)

To prove Wm is a subspace we know we have to show that

(1) 0 vector is in Wm

(2) Given u,v in Wm; then u+v is an element of Wm

(3) Given u in Wm, k in R, then k*u is an element of Wm

I don't know how to prove (2)

I have a problem proving (3), if we choose k in R, if k is negative, then km is negative and we'd have Wm=((km)x,x) with km negative, then ku for some u in Wm is not an element of Wm.

Trying to prove (b)

I have no idea at all.

Thanks for your time.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Prove that Wm is a subspace of R2?

**Physics Forums | Science Articles, Homework Help, Discussion**