# Vector Space help needed

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I've attached the relevant question. I'm not really sure what the steps I need to take are. Do the standard basis vectors work?

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#2

(Original post by

I've attached the relevant question. I'm not really sure what the steps I need to take are. Do the standard basis vectors work?

**pineapplechemist**)I've attached the relevant question. I'm not really sure what the steps I need to take are. Do the standard basis vectors work?

Could you have a guess at the dimension (with reasoning if you can) before I attempt to help? Don't worry about the basis for now.

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(Original post by

The standard basis does not work: (1,0,0) doesn't satisfy the equation, sadly.

Could you have a guess at the dimension (with reasoning if you can) before I attempt to help? Don't worry about the basis for now.

**Smaug123**)The standard basis does not work: (1,0,0) doesn't satisfy the equation, sadly.

Could you have a guess at the dimension (with reasoning if you can) before I attempt to help? Don't worry about the basis for now.

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#4

Geometrically, do you know what type of set the equation

a + 2b - 2c = 0

describes?

a + 2b - 2c = 0

describes?

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**Smaug123**)

The standard basis does not work: (1,0,0) doesn't satisfy the equation, sadly.

Could you have a guess at the dimension (with reasoning if you can) before I attempt to help? Don't worry about the basis for now.

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#6

(Original post by

Would (0,1,1), (1,0,0.5) and (0,-1,-1) form a basis because they satisfy the equation?

**pineapplechemist**)Would (0,1,1), (1,0,0.5) and (0,-1,-1) form a basis because they satisfy the equation?

The fact is, the vector space you are trying to find a basis for does NOT have dimension 3, so you aren't going to be able to find a basis with 3 elements.

It might help to look at it like this:

If you have a vector (a, b, c) in the vector space, then we know that

a+2b-2c = 0.

So suppose you are given a, b. What must c equal? (*)

So we know that (a, b, c) = (a, b, Aa+Bb) where (A, B) are constants you should have found in (*).

Rewrite it as where

**A, B**are constant vectors.

At this point, what can we say about

**A, B**?

Do they span our vector space? (If so, why, if no, why)?

Are they linearly independent?

So...

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(Original post by

(0, 1, 1) + (0, -1, -1) = 0, so these two vectors are not linearly independent.

The fact is, the vector space you are trying to find a basis for does NOT have dimension 3, so you aren't going to be able to find a basis with 3 elements.

It might help to look at it like this:

If you have a vector (a, b, c) in the vector space, then we know that

a+2b-2c = 0.

So suppose you are given a, b. What must c equal? (*)

So we know that (a, b, c) = (a, b, Aa+Bb) where (A, B) are constants you should have found in (*).

Rewrite it as where

At this point, what can we say about

Do they span our vector space? (If so, why, if no, why)?

Are they linearly independent?

So...

**DFranklin**)(0, 1, 1) + (0, -1, -1) = 0, so these two vectors are not linearly independent.

The fact is, the vector space you are trying to find a basis for does NOT have dimension 3, so you aren't going to be able to find a basis with 3 elements.

It might help to look at it like this:

If you have a vector (a, b, c) in the vector space, then we know that

a+2b-2c = 0.

So suppose you are given a, b. What must c equal? (*)

So we know that (a, b, c) = (a, b, Aa+Bb) where (A, B) are constants you should have found in (*).

Rewrite it as where

**A, B**are constant vectors.At this point, what can we say about

**A, B**?Do they span our vector space? (If so, why, if no, why)?

Are they linearly independent?

So...

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#10

Still wrong. You need to write it in the for a

E.g. if you had (a, b, c) = (a, b, 7a + 9b), then you would need to rewrite this as a (1, 0, 7) + b (0, 1, 9).

**A**+ b**B**where**A, B are constant vectors.**(i.e. don't involve a or b).E.g. if you had (a, b, c) = (a, b, 7a + 9b), then you would need to rewrite this as a (1, 0, 7) + b (0, 1, 9).

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(Original post by

Still wrong. You need to write it in the for a

E.g. if you had (a, b, c) = (a, b, 7a + 9b), then you would need to rewrite this as a (1, 0, 7) + b (0, 1, 9).

**DFranklin**)Still wrong. You need to write it in the for a

**A**+ b**B**where**A, B are constant vectors.**(i.e. don't involve a or b).E.g. if you had (a, b, c) = (a, b, 7a + 9b), then you would need to rewrite this as a (1, 0, 7) + b (0, 1, 9).

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#14

Should you not say:

A basis of V is:

linearly independent

spans V

And where you've written a(1,0,1/2) and b(0,1,1) should you not write they form a basis of V.

I think you've gotten a bit confused about R^3 and V. V is a subspace of R^3. Everything else seems right though.

(Although I wouldn't trust this post until someone else confirms...)

A basis of V is:

linearly independent

spans V

And where you've written a(1,0,1/2) and b(0,1,1) should you not write they form a basis of V.

I think you've gotten a bit confused about R^3 and V. V is a subspace of R^3. Everything else seems right though.

(Although I wouldn't trust this post until someone else confirms...)

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