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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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