- #1

LCSphysicist

- 634

- 153

W = {f(t) | f(0) = 2f(1)}

The answer say yes, but i don't know how to prove the neutral element.

The answer say yes, but i don't know how to prove the neutral element.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter LCSphysicist
- Start date

- #1

LCSphysicist

- 634

- 153

W = {f(t) | f(0) = 2f(1)}

The answer say yes, but i don't know how to prove the neutral element.

The answer say yes, but i don't know how to prove the neutral element.

- #2

- 17,655

- 18,377

What would be the zero?W = {f(t) | f(0) = 2f(1)}

The answer say yes, but i don't know how to prove the neutral element.

- #3

LCSphysicist

- 634

- 153

i have no idea :|, the answer is literally "yes", just it.What would be the zero?

- #4

- #5

- 17,655

- 18,377

What does ##f(t)## stand for? A certain number at a point ##t##, or what does it mean?i have no idea :|, the answer is literally "yes", just it.

- #6

What does ##f(t)## stand for? A certain number at a point ##t##, or what does it mean?

My guess is that it is the usual abuse of notation.

- #7

- 17,655

- 18,377

I know. I just want to get the OP think about it. The question is trivial once it is understood, so it is all about understanding, not answering.My guess is that it is the usual abuse of notation.

- #8

LCSphysicist

- 634

- 153

The conjunt of reals Polynomials n deegre or smaller more the nule polynomial.

Yes, indeed is a trivial question, actually it's in a book introductory to linear algebra, but i still don't understand how to prove this item.

- #9

- 17,655

- 18,377

In order to prove this property, you only have to show that zero is in that space. Now what is zero in this context?

The conjunt of reals Polynomials n deegre or smaller more the nule polynomial.

Yes, indeed is a trivial question, actually it's in a book introductory to linear algebra, but i still don't understand how to prove this item.

Another property is to show that if ##f(t) \in W## and ##\lambda \in \mathbb{R}##, then ##\lambda \cdot f(t)## must be in ##W##. If you had shown this, then what if ##\lambda =0##?

- #10

vela

Staff Emeritus

Science Advisor

Homework Helper

Education Advisor

- 15,765

- 2,406

What's a conjunt? What does nule mean? I'm trying to figure out what that sentence was intended to mean.The conjunt of reals Polynomials n deegre or smaller more the nule polynomial.

- #11

WWGD

Science Advisor

Gold Member

- 6,292

- 8,192

I assume the OP may be a native Spanish spraker. "Conjunto" is Spanish for "Set" and "Nulo" is Spanish for null. And for others, I assume, per abuse of notation, f(t) is a function. I assume the 0 vector here would be the 0 function/polynomial.What's a conjunt? What does nule mean? I'm trying to figure out what that sentence was intended to mean.

- #12

vela

Staff Emeritus

Science Advisor

Homework Helper

Education Advisor

- 15,765

- 2,406

Ah, now it makes more sense.

- #13

FactChecker

Science Advisor

Homework Helper

Gold Member

- 7,600

- 3,320

- #14

zinq

- 399

- 118

{f(t) | f(0) = 2f(1)}

then this should be written

{f ∈ V | f(0) = 2f(1)}

and V ought to be defined in terms of what functions it contains (domain, codomain, properties) and what is the field

(Note that I rewrote your "f(t)" as just "f", because f means the function itself that is a vector in V, but f(t) means the value of that function after it has been evaluated at some input t.)

But to decide whether your set is a subspace of V, the things to check is whether a) the sum f + g of two vectors f and g in your set also belongs to the set, and b) whether the product αf of an f in your set by a scalar α ∈

- #15

Stephen Tashi

Science Advisor

- 7,781

- 1,540

W = {f(t) | f(0) = 2f(1)}

The answer say yes, but i don't know how to prove the neutral element.

If you are dealing with a vector space whose elements are functions, the zero vector ( neutral element) must be a function. What function is it?

Perhaps you aren't remembering that there can be constant functions. For example, the function f(x) = 3 is a constant function. It is a function even though its value isn't different for different values of x.

- #16

Eclair_de_XII

- 1,066

- 90

- #17

No. As long as the superspaces have the same "operations".

- #18

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 971

It is "closed under scalar multiplication" and "closed under vector addition".

Here the subset is the set of all functions, f, such that f(0)= 2f(1).

"Closed under scalar multiplication". If a is any number then does af satisfy af(0)= 2af(1)?

"Closed under vector addition". If f satisfies f(0)= 2f(`1) and g satisfies g(0)= 2g(1) does f+ g satisfy f(0)+ g(0)= 2(f(1)+ g(1))?

- #19

LCSphysicist

- 634

- 153

I assume the OP may be a native Spanish spraker. "Conjunto" is Spanish for "Set" and "Nulo" is Spanish for null. And for others, I assume, per abuse of notation, f(t) is a function. I assume the 0 vector here would be the 0 function/polynomial.

Voce acertou, mas eu sou brasileiro XD

You're right, but i am brazillian XD

sorry by my "portuenglish"

- #20

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 971

- #21

MidgetDwarf

- 1,395

- 550

Yes. I also speak Spanish and this is true.I assume the OP may be a native Spanish spraker. "Conjunto" is Spanish for "Set" and "Nulo" is Spanish for null. And for others, I assume, per abuse of notation, f(t) is a function. I assume the 0 vector here would be the 0 function/polynomial.

- #22

WWGD

Science Advisor

Gold Member

- 6,292

- 8,192

But read above where he said he's Brazilian.Yes. I also speak Spanish and this is true.

- #23

Mark44

Mentor

- 36,716

- 8,717

Spanish and Portuguese share a lot of words. Brazilian Portuguese is a dialect of Portuguese.But read above where he said he's Brazilian.

Share:

- Last Post

- Replies
- 2

- Views
- 429

- Replies
- 4

- Views
- 100

- Replies
- 39

- Views
- 1K

- Replies
- 39

- Views
- 1K

- Last Post

- Replies
- 10

- Views
- 1K

- Last Post

- Replies
- 6

- Views
- 831

- Replies
- 19

- Views
- 2K

- Replies
- 10

- Views
- 678

- Last Post

- Replies
- 4

- Views
- 538

- Replies
- 19

- Views
- 1K