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brinethery
 3 years ago
Linear algebra: Determine whether this is a vector space:
The set of all rational numbers, with the usual definitons of addition and scalar multiplication.
brinethery
 3 years ago
Linear algebra: Determine whether this is a vector space: The set of all rational numbers, with the usual definitons of addition and scalar multiplication.

This Question is Closed

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2since a rational number multiplied by an irrational number = irrational number

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Oooh I see. Thank you very much!

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2did u get it? or like pretending like u understood cuz that wasnt so clear

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2I am actually in middle of taking linear algebra and had the same question like 2 weeks ago :)

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2No, I get it. It's not closed under scalar multiplication because you can multiply it by an irrational number and the answer won't be rational.

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2I SERIOUSLY don't get vector spaces at all. It is all so freaking weird.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2lol i know so i got a tutor to come over and we sat for 3 hours and he explained everything and now it is so clear

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2It was too confusing and it was killing my brain

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Nice. My instructor has no life (his officer hours are all over the place) so I think I'll just irritate the hell out of him tomorrow :D.

Callum29
 3 years ago
Best ResponseYou've already chosen the best response.1hmm, maybe you could include the field from which your scalars are from. Usually we talk of 'vector space over F' where F is some field, could be the reals, could be the rationals or could be the complex numbers. If the scalars are from the rationals, then it is a vector space as it will be closed under multiplication and the axioms would hold, if real/complex then no...

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2well i thought that F is all rational numbers

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2and i guess the scaler coud be any real number

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Yeah that's what I was thinking... and that would include decimal numbers so scalar mult. wouldn't hold up.

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Anyway, thanks Pippa. I really need to get some serious oneonone time with someone that really knows what they're doing. The book just doesn't help in this case.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2hehe i agree. So like y dont u get some classmates to help?

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2I will try. I am so shy in that class, it's been 7 weeks now and I haven't talked with anybody.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2ohhhhhhhhh i see. Ya its easier to get a tutor. they know how to explain better but not many ppl are familiar with linear algebra

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2It's mostly guys in the class so I just have to get out of my shell and talk to them. You're right, and the books/lecture notes online can be difficult to follow. Anyway, I won't take up any more of your time. I appreciate your help :)

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.2hehe bye gtg study linear algebra :)

Callum29
 3 years ago
Best ResponseYou've already chosen the best response.1Well in an abstract sense, vectors are simply 'objects' (can be numbers, may not be) which may be added together and multiplied by scalars. In your case, the set \[\mathbb{Q}\] is where your vectors are from, and scalars are from some field F. Vector addition is just field addition, scalar multiplication is just field multiplication, and if that field is the rationals, then you have a vector space! Note that \[\mathbb{Q}\] will have two subspaces which are \[\{0\}\] and itself...

Callum29
 3 years ago
Best ResponseYou've already chosen the best response.1@brinethery do you see why the rationals are a vector space over themselves, but not a vector space over the reals? If I multiply a rational by a rational I get another rational, if I multiply a rational by a real, I do not necessarily get a rational...
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