The vectors

v = $\displaystyle \begin{bmatrix}0\\3\\-6\\ \end{bmatrix}$ $\displaystyle u = \begin{bmatrix}-1\\3\\-22+k\\ \end{bmatrix}$ $\displaystyle w = \begin{bmatrix}-2\\8\\-22\\ \end{bmatrix}$

are linearly independent if and only if k does not equal ______?

Ok so i set up the matrix

$\displaystyle \begin{bmatrix}0&-1&2\\3&3&8\\-6&-22+k&-22\\ \end{bmatrix}$

then i reduced it down to this

$\displaystyle \begin{bmatrix}1&0&\frac{2}{3}\\0&1&2\\0&-16+k&-6\\ \end{bmatrix}$

Not sure what to do now or if i am even headed in the right direction

Thanks for any suggestions.