I showing work for the following questions

  • Thread starter MastersMath12
  • Start date
  • Tags
    Work
In summary: And have you tried plugging in values for u and v in both the real and Z2 cases to see if the conclusion holds?
  • #1
MastersMath12
2
0
1) Which of the following are subspaces of R3

a) T = {(x1, x2, x3) | x1x2x3 = 0}
b) T = {(x1, x2, x3) | x1 - x3 = 0}
c) T = {(x1, x2, x3) | x1 = 0}
d) T = {(x1, x2, x3) | x1 = 1}

2) Let U be a k-vector space, where k is any field. Let V be a subspace of U. Assume that dimk V = dimk U. Show that U = V

3) Let u and v be two linear independant vectors of a real vector space. Show that u + v and u - v are linearly independant. Is the same conclusion true if the vector space was over Za.

4) Let T: U--->V be a linear map. Show that T(0u) = 0v

5) Find an example of vector space V and two subspaces W ⊂ V and Z ⊂ V such that Z ∪ W is not a subspace?

6) Show that T = {a + b√3 | a,b∈T } is a field (a subfield of R). Show that M = {a + b√3 | a,b∈ L} is not a field
 
Physics news on Phys.org
  • #2
Hi MastersMath12,

You need to show us what you have attempted so far.

Also, posts in the homework section need to follow a specific format. See here for more details:

https://www.physicsforums.com/showpost.php?p=4021232&postcount=4

In particular, it's not acceptable simply to post your entire homework assignment and expect people to do it for you. Please limit each thread to one problem, using the correct formatting, and showing what you have attempted so far.
 
  • #3
Sorry, I am new to the forum. Thanks for passing the guidlines along to me.

I have completed and feel very confident in the about questions except these two below

1) Find two linear maps A,B: R2 ---> R2 such that A°B ≠ B°A

I understand how to find the two linear maps, but I am still lost with respect to "such that A°B ≠ B°A"

2) Let u and v be two linear independant vectors of a real vector space. Show that u + v and u - v are linearly independant. Is the same conclusion true if the vector space was over Z2.

For this one, I am just completely confused. I understand the idea of proving they are linearly independant but I am having trouble prooving if the same conclusion would be true over Z2.

I have completed the above questions, but I am still pretty confused on these two. Any help would be greatly appreciated.
 
  • #4
MastersMath12 said:
Sorry, I am new to the forum. Thanks for passing the guidlines along to me.

I have completed and feel very confident in the about questions except these two below

1) Find two linear maps A,B: R2 ---> R2 such that A°B ≠ B°A

I understand how to find the two linear maps, but I am still lost with respect to "such that A°B ≠ B°A"
What linear maps did you find?
2) Let u and v be two linear independant vectors of a real vector space. Show that u + v and u - v are linearly independant. Is the same conclusion true if the vector space was over Z2.

For this one, I am just completely confused. I understand the idea of proving they are linearly independant but I am having trouble prooving if the same conclusion would be true over Z2.
What was your proof for the case of the real vector space?
 

FAQ: I showing work for the following questions

1. Why is it important to show work when solving problems?

Showing work helps to demonstrate the process and reasoning behind your solution, making it easier for others to understand and replicate your work. It also allows for easier identification and correction of mistakes.

2. How should I format my work when showing it?

The format of showing work may vary depending on the type of problem and the specific requirements. However, it is generally recommended to organize your work in a clear and logical manner, using numbered steps or bullet points when necessary.

3. Can I use a calculator or other tools when showing work?

Yes, you can use calculators or other tools when showing your work. However, make sure to clearly label and explain the use of any tools or formulas used in your solution.

4. Do I need to show work for every step, even if it seems obvious?

Yes, it is important to show work for every step to ensure that there are no mistakes and to provide a complete understanding of your thought process. Even if a step seems obvious to you, it may not be as clear to others.

5. How can I improve my work showing skills?

One way to improve your work showing skills is to practice regularly and ask for feedback from others. Additionally, you can also review examples and tips from reliable sources, such as textbooks or online tutorials.

Back
Top