you dropped a minus sign in the third row in the second column.

what you should have ended up with, in the 3,3 position is:

some additional comments:

1) please make an effort to type your questions out. many people will not address problems that are entirely from images.

2) since you divide by k several times in the course of the row-reduction, you should check before-hand that 0 is not a value that makes the set linearly dependent.

3) rather than use the substitution x = 1/k, just get your expression over a common denominator. since this equals 0, you can just consider the numerator, and will not have to substitute back for k when you're done.