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# Is it a subspace? watch

1. Hi, I'm struggling to tell whether the following are subspaces.
If I'm correct, I must show that the zero vector is in the subspace, they're closed under addition and closed under multiplication. It's just I'm not sure how to do this.

For the first one, can we let x1,2,3,4=0 and x5=-1 to show the zero vector exits and then for the second let x1,2,3=0 to show the zero vector exits.

I'm struggling with the next step, Thanks!

2. (Original post by Substitution)
Hi, I'm struggling to tell whether the following are subspaces.
If I'm correct, I must show that the zero vector is in the subspace, they're closed under addition and closed under multiplication. It's just I'm not sure how to do this.

For the first one, can we let x1,2,3,4=0 and x5=-1 to show the zero vector exits and then for the second let x1,2,3=0 to show the zero vector exits.

I'm struggling with the next step, Thanks!
Following what? You haven't posted the question. :-)
3. (Original post by Substitution)
Hi, I'm struggling to tell whether the following are subspaces.
If I'm correct, I must show that the zero vector is in the subspace, they're closed under addition and closed under multiplication. It's just I'm not sure how to do this.

For the first one, can we let x1,2,3,4=0 and x5=-1 to show the zero vector exits and then for the second let x1,2,3=0 to show the zero vector exits.

I'm struggling with the next step, Thanks!
Can you be a little clearer with your question, it's not at all obvious what you're saying.
You're right about the conditions, though it's worth saying that the multiplication is scalar multiplication, and you can combine these conditions to say that if where is the subspace, then we require .
4. (Original post by Zacken)
Following what? You haven't posted the question. :-)
(Original post by joostan)
Can you be a little clearer with your question, it's not at all obvious what you're saying.
You're right about the conditions, though it's worth saying that the multiplication is scalar multiplication, and you can combine these conditions to say that if where is the subspace, then we require .
Sorry! Just edited my first post to include the question
5. (Original post by Substitution)
Sorry! Just edited my first post to include the question
Well for the second, you're correct, but for the first, the zero vector is clearly not in , further setting and the others doesn't mean that this is the zero vector, and further this vector is not in .
6. (Original post by joostan)
Well for the second, you're correct, but for the first, the zero vector is clearly not in , further setting and the others doesn't mean that this is the zero vector, and further this vector is not in .
Oh yes of course, don't know how I cold be so oblivious to that. My bad! Would you be able to direct me to how show its clsoed under addition (for practice) Thanks
7. (Original post by Substitution)
Oh yes of course, don't know how I cold be so oblivious to that. My bad! Would you be able to direct me to how show its clsoed under addition (for practice) Thanks
Write and consider the sum for , you'll need to use the property .
If this is in then this simultaneously shows that is closed under addition and scalar multiplication.

Alternatively you can check these separately, by considering and .
8. (Original post by joostan)
Write and consider the sum for , you'll need to use the property .
If this is in then this simultaneously shows that is closed under addition and scalar multiplication.

Alternatively you can check these separately, by considering and .
Hi, Thanks for explaining that.

Still not sure about knowing whether it is in U. Could you please explain a little further
9. (Original post by Substitution)
Hi, Thanks for explaining that.

Still not sure about knowing whether it is in U. Could you please explain a little further
Well if then

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The text passage is a discussion thread from a student forum, where a student is asking for help in determining if certain sets are subspaces in the context of linear algebra. The student is discussing the conditions for a set to be a subspace and is seeking guidance on how to proceed with the proof.
no_question

the passage does not contain a specific mathematical question that requires a numerical or word problem solution. instead, it is a request for guidance on a proof in linear algebra. therefore, it does not fit the criteria for a mathematical question as defined in the task.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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# Is it a subspace? watch

1. Hi, I'm struggling to tell whether the following are subspaces.
If I'm correct, I must show that the zero vector is in the subspace, they're closed under addition and closed under multiplication. It's just I'm not sure how to do this.

For the first one, can we let x1,2,3,4=0 and x5=-1 to show the zero vector exits and then for the second let x1,2,3=0 to show the zero vector exits.

I'm struggling with the next step, Thanks!

2. (Original post by Substitution)
Hi, I'm struggling to tell whether the following are subspaces.
If I'm correct, I must show that the zero vector is in the subspace, they're closed under addition and closed under multiplication. It's just I'm not sure how to do this.

For the first one, can we let x1,2,3,4=0 and x5=-1 to show the zero vector exits and then for the second let x1,2,3=0 to show the zero vector exits.

I'm struggling with the next step, Thanks!
Following what? You haven't posted the question. :-)
3. (Original post by Substitution)
Hi, I'm struggling to tell whether the following are subspaces.
If I'm correct, I must show that the zero vector is in the subspace, they're closed under addition and closed under multiplication. It's just I'm not sure how to do this.

For the first one, can we let x1,2,3,4=0 and x5=-1 to show the zero vector exits and then for the second let x1,2,3=0 to show the zero vector exits.

I'm struggling with the next step, Thanks!
Can you be a little clearer with your question, it's not at all obvious what you're saying.
You're right about the conditions, though it's worth saying that the multiplication is scalar multiplication, and you can combine these conditions to say that if where is the subspace, then we require .
4. (Original post by Zacken)
Following what? You haven't posted the question. :-)
(Original post by joostan)
Can you be a little clearer with your question, it's not at all obvious what you're saying.
You're right about the conditions, though it's worth saying that the multiplication is scalar multiplication, and you can combine these conditions to say that if where is the subspace, then we require .
Sorry! Just edited my first post to include the question
5. (Original post by Substitution)
Sorry! Just edited my first post to include the question
Well for the second, you're correct, but for the first, the zero vector is clearly not in , further setting and the others doesn't mean that this is the zero vector, and further this vector is not in .
6. (Original post by joostan)
Well for the second, you're correct, but for the first, the zero vector is clearly not in , further setting and the others doesn't mean that this is the zero vector, and further this vector is not in .
Oh yes of course, don't know how I cold be so oblivious to that. My bad! Would you be able to direct me to how show its clsoed under addition (for practice) Thanks
7. (Original post by Substitution)
Oh yes of course, don't know how I cold be so oblivious to that. My bad! Would you be able to direct me to how show its clsoed under addition (for practice) Thanks
Write and consider the sum for , you'll need to use the property .
If this is in then this simultaneously shows that is closed under addition and scalar multiplication.

Alternatively you can check these separately, by considering and .
8. (Original post by joostan)
Write and consider the sum for , you'll need to use the property .
If this is in then this simultaneously shows that is closed under addition and scalar multiplication.

Alternatively you can check these separately, by considering and .
Hi, Thanks for explaining that.

Still not sure about knowing whether it is in U. Could you please explain a little further
9. (Original post by Substitution)
Hi, Thanks for explaining that.

Still not sure about knowing whether it is in U. Could you please explain a little further
Well if then

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 19, 2016
The home of Results and Clearing

### 3,010

people online now

### 1,567,000

students helped last year
Today on TSR

### Took GCSEs this summer?

Fill in our short survey for Amazon vouchers!

### University open days

1. Bournemouth University
Wed, 22 Aug '18
2. University of Buckingham
Thu, 23 Aug '18
3. University of Glasgow
Tue, 28 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams
user
The text passage is a discussion thread from a student forum, where a student is asking for help in determining if certain sets are subspaces in the context of linear algebra. The student is discussing the conditions for a set to be a subspace and is seeking guidance on how to proceed with the proof.

TYPE: NO_QUESTION

The passage does not contain a specific mathematical question that requires a numerical or word problem solution. Instead, it is a request for guidance on a proof in linear algebra. Therefore, it does not fit the criteria for a mathematical question as defined in the task.