- #1
krozer
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I need help with this problem that I don't know how to solve.
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.
None.
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.
Homework Statement
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.
Homework Equations
None.
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.
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