posted by Axel .
For which real values of x do the following vectors form a linearly dependent set in R3?
v1= (x, -1/9, -1/9)
v2= (-1/9, x, -1/9)
v3= (-1/9, -1/9, x)
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:
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.