Finding k for Linear Dependence in a Vector Space

[Cyannaca]

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 independent. If w1 = v1 + kv2, w2= v2 - 2kv3 and w3= v3 - 4kv, find k so w1, w2, w3 are linearly independent.

I tried it and got k=0 and I think it's wrong

 

[snoble]

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 dependent.

 

[Cyannaca]

W3 is equal to v3 -4v1. I typed too fast. But anyway, thanks for your help I finally understood the problem.