Question

Why is W not a subspace of the vector space?
W is the set of all linear functions ax+b in c(continous functions)

Answer 1

I dont know if that made sense but in simpler english W a linear function isnt a subspace of continous functions

Answer 2

idk y cuz linear functions are continous so liek it is weird

Answer 3

I think basically it wants you to figure out somehow how this linear function isnt a linear function either when multiplied by a scalar or when added to another function

Answer 4

is it specifically the set of all functions of degree 1 ?

Answer 5

...or is anything less that degree 1 allowed ?

Answer 6

umm idk it says ax+b where a cant equal 0

Answer 7

the only thing I can think is that this is specifically the set of all polynomials of degree exactly 1, and we may have the situation\[ax+b+(-ax)+c=b+c\]which would take it out if that space by lowering the degree
if a and b can't be zero then we're done :D

Answer 8

but that's different than what you said....
ax+b can't be 0 you say?
what's that mean? lol

Answer 9

no "a" can't equal 0

Answer 10

oh, then we're done

Answer 11

ok Thanks :D

Answer 12

Look who's back :P

Answer 13

Hey

Answer 14

Howz it going?

Answer 15

its going wish it wld be better but it is fine

Answer 16

I'm already done with my course :P

Answer 17

Oh well I am very far behind :D

Answer 18

Yeah, next time, you should hang out with me when taking classes.

Answer 19

Well i may be taking a break next term I may just take one course

Answer 20

I dont really like linear algebra

Answer 21

Calc is easy and fun it is more concrete while this is abstract for me

Answer 22

lol

Answer 23

Oh we r bothering turing Sorry

Answer 24

Yeah I feel the same way
only since I started using this site have I felt more comfortable with it
the result of practice of course

Answer 25

linear algebra I mean*

Answer 26

I am gonna take abstract algebra one of these days and like i am nervous

Answer 27

I know my brain wont be able to follow that

Answer 28

I've never even looked at that myself...

Answer 29

Turing I have another question

Answer 30

Turing found this great page
http://tutorial.math.lamar.edu/Classes/LinAlg/VectorSpaces.aspx

The key fact for W not being a subspace is
it says ax+b where a cant equal 0

to be a subspace, we need to satisfy a bunch of axioms, including
There is a special object in V, denoted 0 and called the zero vector, such that for all u in V we have u+0=u

so we need f(x)+ 0 = f(x)
where 0 is in W. Of course, in this context, 0= 0x+0, which is not allowed because a cannot be 0. So W fails with this property

Answer 31

So u r saying something diff than turing

Answer 32

You r saying that a diff axiom fails

Answer 33

You can fail for more than one reason. But when I went through the list given in the link, it looks like W fails with (e) and (f)

Answer 34

okkkkk I see

Answer 35

I have one more that i dont understand

Answer 36

W is a set of all vectorsin R^3 whose compnents are pythagorean triple

Answer 37

doesn't that fail for u+v is in W
e.g. given u= (3,4,5), v= (5,12,13)
is (8,16,18) in W?

Answer 38

phi is saying the same thing more articulately

Answer 39

kkk i get it

Answer 40

ok Thanks guys :D U r awesome