• Support PF! Buy your school textbooks, materials and every day products Here!

Prove a set of vectors is linearly independent

  • #1

Homework Statement


Suppose that {v1,...,vn} is a linearly independent set in a vector space V and let L:V --> W be a one-to-one linear mapping. Prove that {L(v1),...,L(vn)} is linearly independent.


Homework Equations


None


The Attempt at a Solution


If L is a one-to-one linear mapping, then it maps a specific vector in V to a specific vector in W, therefore, {L(v1),...,L(vn)} must be a linearly independent set of vectors.
However, this is not the rigorous proof that the question is looking for.
I will appreciate any help possible, thank you~~~
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
Hint: a set {u1, ..., un} of vectors is linearly independent iff the equation
a1 u1 + ... + an un = 0
can only be satisfied by a1 = a2 = ... = an = 0.
 

Related Threads for: Prove a set of vectors is linearly independent

Replies
6
Views
2K
  • Last Post
Replies
3
Views
930
Replies
1
Views
648
Replies
4
Views
1K
Replies
14
Views
2K
Replies
3
Views
2K
  • Last Post
Replies
8
Views
1K
Replies
7
Views
1K
Top