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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!

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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 $0$.

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Thank you very much, joriki! – Chris Mar 18 '12 at 14:42
@Chris: You're welcome! – joriki Mar 18 '12 at 14:52

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