Solve Vector Space Question: Get the Solution Now

In summary, the user is asking for help with a math question and the helper is requesting that they show their progress so far. The user has shared their thoughts and approach for parts 2a and 2b, but is still struggling to find a solution. The helper then provides a potential method for solving the question by considering the linear transformation and showing that the vectors are independent.
  • #1
LearnerJr
4
0
View attachment 6276

How do you solve this question I just need a solution
 

Attachments

  • image.jpeg
    image.jpeg
    18.8 KB · Views: 70
Physics news on Phys.org
  • #2
Hello LearnerJr and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
  • #3
greg1313 said:
Hello LearnerJr and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

Yes of course. For 2a I know a bit of indirect proof and assume the result
Is not true. But not sure still how to perceive this question in the long run.
2b I know if it's a basis it's vectors have to be linearly independent, they span V.but I still can't solve it.
 
  • #4
Consider the equation $af(v_1)+ bf(v_2)+ cf(v_3)= 0$. In order to show that $f(v_1)$, $f(v_2)$, and $f(v_3)$ are independent we must show that a= b= c= 0.

Since f is a linear transformation, $af(v_1)+ bf(v_2)+ cf(v_3)= f(av_1+ bv_2+ cv_3)= 0$. Since the kernel of f is only the 0 vector, we must have $av_1+ bv_2+ cv_3= 0$. But we were given that $v_1$, $v_2$, and $v_3$ are independent so a= b= c= 0 as we wished.
 

FAQ: Solve Vector Space Question: Get the Solution Now

1. What is a vector space?

A vector space is a mathematical concept that refers to a set of objects, called vectors, that can be added together and multiplied by numbers to produce new vectors. It is an abstract mathematical structure that is used to model real-world phenomena such as forces, velocities, and other physical quantities.

2. What is a vector space question?

A vector space question is a question that involves finding a solution in a vector space. This could involve determining whether a set of vectors form a vector space, finding the basis of a vector space, or solving linear equations in a vector space.

3. How do I solve a vector space question?

To solve a vector space question, you will need to understand the properties of vector spaces and know how to apply them to the specific problem at hand. This may involve using techniques such as Gaussian elimination, finding the span of a set of vectors, or determining linear independence.

4. Why is solving vector space questions important?

Solving vector space questions is important because vector spaces are fundamental mathematical structures that have many applications in physics, engineering, and computer science. Being able to solve vector space questions allows us to understand and model real-world problems more accurately and make more accurate predictions.

5. Can I use software to solve vector space questions?

Yes, there are many mathematical software programs that can help you solve vector space questions. These programs can perform calculations and graphing, making it easier to visualize and understand the solutions. However, it is important to have a solid understanding of the concepts involved in vector spaces before relying solely on software.

Similar threads

Replies
8
Views
1K
Replies
7
Views
1K
Replies
3
Views
1K
Replies
2
Views
2K
Replies
15
Views
2K
Back
Top