Posted by Axel on Friday, November 27, 2009 at 2:05pm.
The vectors form a linearly dependent set in ℜ3 if the determinant of the matrix formed by the three vectors is zero.
Evaluate the determinant:
|x,k,k|
|k,x,k|
|k,k,x|
in terms of x and k, where k can eventually substituted for -1/9.
Solve the resulting cubic equation for x in terms of k. It actually factors nicely into (x+?)(x-??)².
In fact, you should be able to determine ?? by inspection.
Post if you need more help.
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