Asked 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)
v1= (x, -1/9, -1/9)
v2= (-1/9, x, -1/9)
v3= (-1/9, -1/9, x)
Answers
Answered by
MathMate
The vectors form a linearly dependent set in ℜ<sup>3</sup> 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.
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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