Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let ${w*(80/27,-76/27,-31/27)} $ be the solution set of a homogeneous system of linear equations.

The statement to be decided if it's true or false, is this:

The solution set of the given system, contains at least one linearly independent element

As I got, using wolfram with this query:

linear independence (1,2*w)

(and got this)

(1, 2 w) is linearly independent

What is the point of talking about linear independence for 1 element?

Also, could the statement be false, due to the fact that the linearly independent is only one and not at least one?

Thank you!

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

The definition of linear independence holds for one element as it does for any other number of elements. An element $v$ is linearly independent if $cv=0$ with $c$ a scalar implies $c=0$. Thus the only linearly dependent element is $0$.

share|improve this answer
    
Thank you very much, joriki! –  Chris Mar 18 '12 at 14:42
    
@Chris: You're welcome! –  joriki Mar 18 '12 at 14:52
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.