are linearly independent if and only if k=/

Question

The vectors v=[-2 -1 -5] , u=[2 -2 -8+k] and w= [4 -7 1] are linearly independent if and only if k=/

Answer 1

If determinant det([- 2, - 1, - 5] [2, - 2, - 8 + k] [4 -7 1] ≠ 0;

So 4 + 70 + 32 - 4k - 40 + 2 + 112 - 18k ≠ 0; 180 - 18k ≠ 0. k ≠ 10.

If k ≠ 10 then given vectors u, v and w are linearly independent.