v=(6, -3, 0)
u=(-3, 5, -7)
w=(9, 6, k)
what real number can't k be for the vectors to be linearly independent?
set up the augmented matrix: $\displaystyle \left( \begin{array}{ccc} \left[ \begin{array}{c} v_1 \\ v_2 \\ v_3 \end{array} \right] & \left[ \begin{array}{c} u_1 \\ u_2 \\ u_3 \end{array} \right] & \left[ \begin{array}{c} w_1 \\ w_2 \\ w_3 \end{array} \right] \end{array} \right) $. equate it to zero and solve the system. the k for which the system only has the trivial solution is linearly independent