Are These Vectors Linearly Independent?

In summary, this question asked about how to calculate a determinant, which is a theorem that is relevant to linear independence.
  • #1
woundedtiger4
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Hi everyone!
It was the question given to us in today's test & I was wondering if anyone can tell me what is the correct answer. The teacher will post the answers by the end of this week but I am feeling anxious to know the answer.

Thanks in advance.

P.S. Sorry, if I have posted the question in wrong section of this website.
 
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  • #2
Questions about textbook-style problems should be posted in a homework forum. I will move this thread there. Our rules about homework say that we can't help unless you show us your solution, or at least your work up to the point where you're stuck.
 
  • #3
Fredrik said:
Questions about textbook-style problems should be posted in a homework forum. I will move this thread there. Our rules about homework say that we can't help unless you show us your solution, or at least your work up to the point where you're stuck.

It was a question from my today's test which was multiple choice question styled. My lecturer said he will provide the solution later this week therefore I was worried about my answer and asked for help as I selected the option "d".
I wrote the at the of the post if my thread is in wrong section of website.

Edited note: I can provide the whole question paper which shows today's date and institution's name, just to make sure it is not from weekly assignment.
 
  • #4
woundedtiger4 said:
It was a question from my today's test which was multiple choice question styled. My lecturer said he will provide the solution later this week therefore I was worried about my answer and asked for help as I selected the option "d".
I wrote the at the of the post if my thread is in wrong section of website.

Edited note: I can provide the whole question paper which shows today's date and institution's name, just to make sure it is not from weekly assignment.
WHY did you answer "d" ? You are apparently not understanding that on this forum we don't give answers we help people figure out how to get the answer themselves. Show your work, explain your reasoning, and then we can either tell you you got it right or give hints for what you might have done wrong.
 
  • #5
woundedtiger4 said:
Edited note: I can provide the whole question paper which shows today's date and institution's name, just to make sure it is not from weekly assignment.
Wouldn't it be just as easy to show us your attempt to solve the problem? You don't even have to use LaTeX to type this. Here's a λ that you can copy and paste.
 
  • #6
woundedtiger4 said:
I selected the option "d".
On what logic?
Do you know how to calculate a determinant, and how that would be relevant here?
(Please make your titles more informative in future. Here you could have mentioned linear independence.)
 
  • #7
The determinant approach requires you to understand a somewhat complicated theorem. I prefer to just use the definition of "linearly independent".

I have to get up early tomorrow, so I'm going to bed. But I'm sure someone else will help you if you post your attempt to solve the problem.
 
  • #8
I am closing this thread. As already mentioned, homework or coursework questions need to be posted in the Homework & Coursework sections (where the thread was moved to). Also, you need to show the work you have done. In this case, that would be the reasoning behind your choice of 'd' as the answer.

Please start a new thread, with an informative title ("Please help" is NOT informative) and your reasoning for your answer.
 

Related to Are These Vectors Linearly Independent?

1. What are linearly independent vectors?

Linearly independent vectors are a set of vectors in a vector space that do not have a linear relationship with each other. This means that none of the vectors can be expressed as a linear combination of the others.

2. How do you determine if a set of vectors is linearly independent?

To determine if a set of vectors is linearly independent, you can use the method of Gaussian elimination or row reduction to create an augmented matrix. If the matrix can be reduced to an identity matrix, then the vectors are linearly independent. If the matrix has any rows of all zeros, then the vectors are linearly dependent.

3. What is the importance of linearly independent vectors?

Linearly independent vectors are important in linear algebra because they form a basis for a vector space. This means that any vector in the space can be expressed as a linear combination of the basis vectors. Linear independence also allows for easier computation and analysis of vector operations.

4. Can a set of vectors be both linearly independent and linearly dependent?

No, a set of vectors can only be either linearly independent or linearly dependent. If a set of vectors is linearly dependent, it means that at least one vector can be expressed as a linear combination of the others. In this case, the set is not linearly independent.

5. How many linearly independent vectors can a vector space have?

The number of linearly independent vectors that a vector space can have is equal to its dimension. For example, a 2-dimensional vector space will have a maximum of 2 linearly independent vectors. A 3-dimensional vector space will have a maximum of 3 linearly independent vectors, and so on.

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