Finding k for Linear Dependence in a Vector Space

In summary, the conversation is about finding the value of k in order for the vectors w1, w2, and w3 to be linearly dependent. The process involves forming a matrix with the w vectors and using the determinant to solve for k. The typo in the original problem was corrected and the issue was resolved with the help of the expert's explanation.
  • #1
Cyannaca
22
0
I would really appreciate if anyone could help me with this problems.

V is a vector space on R and v1, v2, v3 e V are linearly independant. If w1 = v1 + kv2, w2= v2 - 2kv3 and w3= v3 - 4kv, find k so w1, w2, w3 are linearly dependant.

I tried it and got k=0 and I think it's wrong :mad:
 
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  • #2
Hmm... I think you have a typo you need to fill. what does w3 equal. is it v3-4kv1 or v3-4kv2 or something else. What you want to do is form a matrix where the each column is a w vector and the row represents how many of each v vector makes up the w vector. For example the first column represents w1 and is [1, k, 0] since w1 = 1*v1+ k*v2 + 0*v3. Then take the determinant and figure out for which k the determinant is 0. Those are the k's where the w's are linearly dependant.
 
  • #3
W3 is equal to v3 -4v1. I typed too fast. But anyway, thanks for your help I finally understood the problem.
 

Related to Finding k for Linear Dependence in a Vector Space

What is a vector space?

A vector space is a mathematical concept that represents a set of objects called vectors, which can be added together and multiplied by numbers to create new vectors.

What is the "vector space problem"?

The vector space problem is a common issue in linear algebra that involves finding a set of vectors that span a given vector space. This can help to understand the structure and properties of the space.

How can I solve the vector space problem?

To solve the vector space problem, you can use various techniques such as Gaussian elimination, finding a basis for the space, or using linear combinations of known vectors to create new ones.

Why is the vector space problem important?

The vector space problem is important because it helps to understand the structure and behavior of vector spaces, which have many applications in fields such as physics, engineering, and computer science.

What are some real-life examples of vector spaces?

Some real-life examples of vector spaces include the 3D space in which we live, the space of all possible colors, the space of all possible sound waves, and the space of all possible mathematical functions.

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