# Determine if subset is subspace of R3. Need Help.

• digitol87
In summary, to determine if a subset of R3 is a subspace, you must use the addition and multiplication closure methods. The set {[x,y,z] | x,y,z in R, z = 3x+2} does not contain the zero vector (0, 0, 0) as it does not satisfy z = 3x + 2. To apply the addition method, you must show that the sum of two elements in the set is also in the set, and for the multiplication method, it must be true that if v is in the set, then kv is also in the set. This distinction is important when considering vectors in the subset versus vectors in R3.
digitol87
1. {[x,y,z] | x,y,z in R, z = 3x+2}.
How do I determine if this subset is a subspace of R3? Am I wrong when I say this set contains the zero vector? If this is the case, then I have to use the addition and multiplication closure methods, right?

Thanks

digitol87 said:
{[x,y,z] | x,y,z in R, z = 3x+2}.
How do I determine if this subset is a subspace of R3? Am I wrong when I say this set contains the zero vector?
Yes, wrong. (0, 0, 0) does not satisfy z = 3x + 2.
digitol87 said:
If this is the case, then I have to use the addition and multiplication closure methods, right?

Thanks

Mark44 said:
Yes, wrong. (0, 0, 0) does not satisfy z = 3x + 2.

OK, That's a good first step. I'm still a little confused as to how to apply the addition method.
can I add [x,y,z] + [a,b,c] then get [x+a, y+b, z+c] ? Then what?

Thanks.

No, you have to take two elements in the set, and show that their sum is in the set. You can't take any old arbitrary vector in R3. Also, it must be true that if v is an element in the set, then kv is also in the set.

What must be true for any element in your set? I.e., how do you distinguish between vectors in your set and plain old vectors in R3?

## 1. What is a subset?

A subset is a set that contains elements of another set. In other words, all the elements in the subset are also present in the larger set.

## 2. How do you determine if a subset is a subspace of R3?

In order to determine if a subset is a subspace of R3, it must meet three criteria: it must contain the zero vector, it must be closed under addition, and it must be closed under scalar multiplication.

## 3. What is the zero vector?

The zero vector is a vector that has all of its components equal to zero. In R3, the zero vector would be represented as (0, 0, 0).

## 4. How do you check if a subset is closed under addition?

To check if a subset is closed under addition, you can take any two elements from the subset and add them together. If the resulting vector is also in the subset, then the subset is closed under addition.

## 5. Can a subset of R3 be a subspace if it does not contain the zero vector?

No, a subset of R3 cannot be a subspace if it does not contain the zero vector. The zero vector is a necessary component for a subset to be considered a subspace of R3.

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