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!