subspaces

[mental echo]

I don't really get why the 2nd answer is not a subspace of R^3. The solution was that it wasn't closed under scalar multiplication. I mean R^3 basically contains every single vector so all vectors with integer components should be a subspace of it

[knotty tendon]

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[coral sinew]

[1,1,1] is in the set, but q[1,1,1] isnt for any non-integer real number

so it's not closed under scalar multiplication

yes it's a subset, but it doesnt meet all the conditions on being a subspace

[mental echo]

oh wait so scalars can have decimals

[coral sinew]

R^3 is a real vector space

the scalars are R

and there most definitely exists real numbers that arent integer / multiplies an integer to get an integer

like 1/2[2,2,2] is in the set, but 1/2[1,1,1] isnt

the 1/2[1,1,1] not being in the set means it cant be closed under scaling

since the scaling map sends (1/2,[1,1,1]) to something outside the integer lattice

[mental echo]

ok i get it now thank you

+close