Quick Subspace Question: Understanding A = [x+1,0] as a Potential Subspace

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In summary: Yeah, you are probably thinking too hard. The set of vectors [x+1,0] is really the same thing as the set of vectors [x',0]. Where x'=x+1. Where both x and x' can be any real number.
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I Like Pi
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Homework Statement


Hey, I'm trying to figure out whether A = [x+1,0] is a subspace... I know it's probably simple but what I'm confused is that...

Homework Equations


The Attempt at a Solution


u+v must be an element of A. let u = [x1+1,0] and v=[x2+1,0]. Adding them together gives you [x1+x2+2,0], where (x1+x2) = x. Therefore it wouldn't be a subspace because you now have the form [x+2,0] which is not the same?

But if I look at it, [x1+x2+2,0] should be a subspace because you can get the same value with [x+1, 0] (let x1, x2 = -1 and let x = -1, both get 0 vector, for example)
Thanks for any help!
 
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  • #2
I think your second answer is closer. You want to show [x+1,0] is a subspace of R^2 if I understand what you are asking. What things do you have show to prove A is a subspace? And yes, [x1+x2+2,0]=[(x1-1+x2)+1,0]. So it is closed under addition if I've understood you correctly.
 
  • #3
Dick said:
What things do you have show to prove A is a subspace? And yes, [x1+x2+2,0]=[(x1-1+x2)+1,0]. So it is closed under addition if I've understood you correctly.

Well I know the three conditions. However, what I'm not getting is that you should have your u+v in the form [x+1,0], where x is made up of x1 + x2, or am I getting the definition wrong? In this case i have (x1 + x2 + 1)...
 
  • #4
[x1+x2+2,0]=[(x1+1+x2)+1,0] is in the form [x+1,0] where x=x1+1+x2 as you said, isn't it? Sorry, I had a typo in the previous post.
 
  • #5
Dick said:
[x1+x2+2,0]=[(x1+1+x2)+1,0] is in the form [x+1,0] where x=x1+1+x2, isn't it? Sorry, I had a typo in the previous post.

Oh yeah! So you can rearrange it anyway so that you get the correct form? I thought that the initial variable had to be represented by only variables (if that makes sense)...
 
  • #6
I Like Pi said:
Oh yeah! So you can rearrange it anyway so that you get the correct form? I thought that the initial variable had to be represented by only variables (if that makes sense)...

Yeah, you are probably thinking too hard. The set of vectors [x+1,0] is really the same thing as the set of vectors [x',0]. Where x'=x+1. Where both x and x' can be any real number.
 

What is a Quick Subspace Question?

A Quick Subspace Question is a mathematical or scientific question that can be answered quickly using the principles of subspace, which is a subset of a vector space.

How can Quick Subspace Questions be useful in scientific research?

Quick Subspace Questions can be useful in scientific research because they allow researchers to quickly analyze and solve problems related to vector spaces, which are often used in fields such as physics, engineering, and computer science.

Can Quick Subspace Questions be applied in real-world scenarios?

Yes, Quick Subspace Questions can be applied in real-world scenarios. For example, they can be used to optimize the placement of antennas in a wireless network or to analyze the performance of a mechanical system.

Do I need to have a strong background in mathematics to understand Quick Subspace Questions?

While a strong background in mathematics can be helpful, Quick Subspace Questions can also be understood by individuals with a basic understanding of vector spaces and linear algebra.

Are there any resources available for learning about Quick Subspace Questions?

Yes, there are many resources available for learning about Quick Subspace Questions, including textbooks, online tutorials, and interactive tools. Additionally, many universities offer courses on linear algebra and vector spaces which cover Quick Subspace Questions.

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