# Parametric equation in subspace

• negation
In summary, The subset S of R3, given by x = 1-4t, y = -2-t, z = -2-t, is not a subspace of R3 because there is no value of t for which (1-4t, -2-t, -2-t) is equal to (0, 0, 0). Therefore, it does not meet the first requirement of a subspace, which is to contain the zero vector.
negation

## Homework Statement

The following describes a subset S of R3, you are asked to decide if the subset is a subspace of R3.

x = 1-4t
y = -2-t
z = -2-t

## The Attempt at a Solution

R3 = {(1-4t, -2-t, -2-t) | t element of all Real number}If S is a subset, at least one must be true.

1) must contain zero vector
2) Sum of any 2 members in S can be found in S
3) scalar multiple of any member in S can be found in S

y + z = -2-t + (-2-t) =/=0

S is not a subset of R3.

negation said:

## Homework Statement

The following describes a subset S of R3, you are asked to decide if the subset is a subspace of R3.

x = 1-4t
y = -2-t
z = -2-t

## The Attempt at a Solution

R3 = {(1-4t, -2-t, -2-t) | t element of all Real number}

If S is a subset, at least one must be true.

S plainly is a subset of $\mathbb{R}^3$. For S to be a subspace, all three of the following must be true:

1) must contain zero vector
2) Sum of any 2 members in S can be found in S
3) scalar multiple of any member in S can be found in S

On the other hand, if S is not a subspace then at least one of those is false.

y + z = -2-t + (-2-t) =/=0

Concentrate on the first requirement: is there a $t \in \mathbb{R}$ for which $1 - 4t = -2 - t = 0$?

1 person
pasmith said:
S plainly is a subset of $\mathbb{R}^3$. For S to be a subspace, all three of the following must be true:

On the other hand, if S is not a subspace then at least one of those is false.

Concentrate on the first requirement: is there a $t \in \mathbb{R}$ for which $1 - 4t = -2 - t = 0$?

Yes there is a t = 1

Why doesn't that help me? Zero vector right?

I don't know what you mean by "Zero vector, right?". If you mean you are trying to show that the zerol vector is not in this set then you need to look at (1- 4t, -2- t, -2- t)= (0, 0, 0). That was why pasmith asked "is there a t for which 1- 4t= -2- t= 0?" Showing that y+ z is not identically 0 doesn't tell you anything.

And no, t= 1 does NOT make 1- 4t= -2- t= 0.

HallsofIvy said:
I don't know what you mean by "Zero vector, right?". If you mean you are trying to show that the zerol vector is not in this set then you need to look at (1- 4t, -2- t, -2- t)= (0, 0, 0). That was why pasmith asked "is there a t for which 1- 4t= -2- t= 0?" Showing that y+ z is not identically 0 doesn't tell you anything.

And no, t= 1 does NOT make 1- 4t= -2- t= 0.

There's no t value for which 1-4t = -2-t = 0

That was nonsensical-just feeling really stressed out with all the work.

Yes, there is no value of t for which 1- 4t= -2- t= 0 which means that (1- 4t, -2- t, -2- t) is never equal to (0, 0, 0). The zero vector is not in this set.

1 person
HallsofIvy said:
Yes, there is no value of t for which 1- 4t= -2- t= 0 which means that (1- 4t, -2- t, -2- t) is never equal to (0, 0, 0). The zero vector is not in this set.

Understood.

## 1. What is a parametric equation in subspace?

A parametric equation in subspace is a mathematical representation that describes the coordinates of a point or set of points in a subspace using one or more parameters. It is often used to simplify complex geometric shapes or curves in higher dimensions.

## 2. How is a parametric equation in subspace different from a regular equation?

A regular equation typically describes the relationship between two variables, such as x and y. A parametric equation in subspace, on the other hand, describes the coordinates in terms of one or more parameters, which can vary independently from each other.

## 3. What are the advantages of using parametric equations in subspace?

Parametric equations in subspace allow for a more concise and elegant representation of complex geometries. They also make it easier to manipulate and analyze these shapes, as the parameters can be adjusted to see how the shape changes. Additionally, parametric equations are often used in computer graphics and animation.

## 4. How are parametric equations in subspace used in real-world applications?

Parametric equations in subspace have many practical applications, such as in engineering, physics, and computer science. They are used to model and analyze complex systems, such as the motion of objects in space, the behavior of fluids, and the design of computer-generated images.

## 5. Are there any limitations to using parametric equations in subspace?

One limitation of parametric equations in subspace is that they can only represent points or curves within the subspace they are defined in. They cannot account for points outside of this space. Additionally, parametric equations can become more complex and difficult to interpret as the dimensions of the subspace increase.

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