Posted by **Axel** on Friday, November 27, 2009 at 2:05pm.

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)

- Math -
**MathMate**, Friday, November 27, 2009 at 7:03pm
The vectors form a linearly dependent set in ℜ^{3} 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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