# Homework Help: Linear independence

1. Jan 18, 2010

### EV33

1. The problem statement, all variables and given/known data
If the set {v1,v2,v3} of vectors in R^(m) is linearly dependent, then argue that the set {v1,v2,v3,v4} is also linearly dependent for every choice of v4 in R^(m).

2. Relevant equations
Definitions would be more relevant so...

Linearly Independent: If the only solution is the trivial solution

Linearly Dependent: If there are more solutions than he trivial solution.

3. The attempt at a solution

I started out by writing out three vectors that are a dependent set, and I noticed that no matter what I added for v4 there would still be that non trivial solution, therefore making it remain dependent.

Is that sound reasoning?

2. Jan 18, 2010

### tiny-tim

Hi EV33!

(try using the X2 and X2 tags just above the Reply box )
If I'm guessing correctly what you mean, then yes that's sound.

But you should write it properly, starting "if v1 v2 and v3 are dependent, then there exist …"

3. Jan 18, 2010

### EV33

Thank you very much