Finding N(T) and R(T): Solving a Linear Transformation Problem

  • Thread starter pyroknife
  • Start date
In summary, the problem involves finding a basis for the null space of a linear transformation T that transforms a vector space V to R^2. The book defines the null space as the set of vectors in V that are mapped to 0 by T. The task is to find a T that maps a vector v to 0. The person asking for help is confused and seeking a hint for how to approach the problem. They mention having experience with similar problems but this one has them stumped.
  • #1
pyroknife
613
3
Alright this problem has really gotten me confused. I skipped 1 and 2 because I know how to do those, but 3 and 4, I do not.

I think the problem statement is saying the linear transformation transforms the vector space V to R^2. and it's defined by T(f)=...

For 3) find a basis for N(T)

The book defines N(T) as = {v ε V l T(v)=0}
So I must find T such that T(v)=0.


I have no clue how to do this problem. can someone give me a hint?
I've looked at other types of problems where we find a basis for N(T) and those seem easy, but this one just got me confused.

What is f?
 
Physics news on Phys.org
  • #2
pyroknife said:
Alright this problem has really gotten me confused. I skipped 1 and 2 because I know how to do those, but 3 and 4, I do not.

I think the problem statement is saying the linear transformation transforms the vector space V to R^2. and it's defined by T(f)=...

For 3) find a basis for N(T)

The book defines N(T) as = {v ε V l T(v)=0}
So I must find T such that T(v)=0.

I have no clue how to do this problem. can someone give me a hint?
I've looked at other types of problems where we find a basis for N(T) and those seem easy, but this one just got me confused.

What is f?
Where are the problems?

I see none !

Added in Edit:

Here it is:

attachment.php?attachmentid=52421&d=1351485538.png
 
Last edited:
  • #3
SammyS said:
Where are the problems?

I see none !

SammyS said:
Where are the problems?

I see none !

Oh sorry.
 

Attachments

  • Untitled.png
    Untitled.png
    25.9 KB · Views: 528

1. What is the purpose of finding N(T) and R(T)?

The purpose of finding N(T) and R(T) is to understand the behavior of a system at different temperatures. N(T) refers to the number of particles in a system at a given temperature, while R(T) refers to the rate of reactions or transformations within the system at that temperature. By studying these values, scientists can gain insight into the thermodynamic properties and kinetics of a system.

2. How do you determine N(T) and R(T)?

N(T) and R(T) can be determined through experimental methods such as measuring the number of particles in a system or tracking the rate of a reaction at different temperatures. These values can also be calculated using mathematical models and equations based on thermodynamic principles.

3. What factors affect N(T) and R(T)?

N(T) and R(T) can be affected by a variety of factors, including temperature, pressure, and the composition and properties of the system. Changes in these variables can alter the number of particles present and the rate of reactions or transformations within the system.

4. How can knowledge of N(T) and R(T) be applied in real-world situations?

Knowledge of N(T) and R(T) can be applied in a wide range of fields, from materials science and engineering to chemistry and biology. For example, understanding the behavior of a material at different temperatures can help in designing more efficient and durable products, while knowledge of reaction rates can aid in developing new drugs or optimizing industrial processes.

5. Are there any limitations to using N(T) and R(T) in scientific research?

Like any scientific measurements or calculations, there are limitations to using N(T) and R(T) in research. These values are dependent on the accuracy of the experimental methods and mathematical models used, and may not always accurately represent the behavior of a system in real-world conditions. It is important for scientists to carefully consider and account for these limitations in their research.

Similar threads

Null space of dual map of T = annihilator of range T
    • Calculus and Beyond Homework Help
Replies
0
Views
449
Direct Proof that every zero of p(T) is an eigenvalue of T
    • Calculus and Beyond Homework Help
Replies
24
Views
793
Prove that range ##T'## = ##(\text{null}\ T)^0##
    • Calculus and Beyond Homework Help
Replies
1
Views
456
Tricky Problem: Prove range T = null ##\phi## when null T' has dim 1
    • Calculus and Beyond Homework Help
Replies
8
Views
619
Avoid unpleasant integrals in solving IVP
    • Calculus and Beyond Homework Help
Replies
3
Views
569
Given surjective ##T:V\to W##, find isomorphism ##T|_U## of U onto W.
    • Calculus and Beyond Homework Help
Replies
1
Views
606
Prove that the linear space is infinite dimensional
    • Calculus and Beyond Homework Help
Replies
18
Views
1K
Linear transformation: Find the necessary quantity of T
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Given specific v, dimension of subspace of L(V, W) where Tv=0?
    • Calculus and Beyond Homework Help
Replies
14
Views
592
Solving differential equation (t^2-1)y''-6y=1
    • Calculus and Beyond Homework Help
Replies
2
Views
187

Hot Threads

Recent Insights

Back
Top