Answer
$${\text{ }}{\bf{z}} = \left\langle { - 3,4,20} \right\rangle $$
Work Step by Step
$$\eqalign{
& {\text{Let }}{\bf{u}} = \left\langle {1,2,3} \right\rangle ,{\text{ }}{\bf{v}} = \left\langle {2,2, - 1} \right\rangle ,{\text{ }}{\bf{w}} = \left\langle {4,0, - 4} \right\rangle \cr
& {\text{Find }}{\bf{z}} = 5{\bf{u}} - 3{\bf{v}} - \frac{1}{2}{\bf{w}} \cr
& {\text{ }}{\bf{z}} = 5\left\langle {1,2,3} \right\rangle - 3\left\langle {2,2, - 1} \right\rangle - \frac{1}{2}\left\langle {4,0, - 4} \right\rangle \cr
& {\text{Solve and simplify}} \cr
& {\text{ }}{\bf{z}} = \left\langle {5,10,15} \right\rangle - \left\langle {6,6, - 3} \right\rangle - \left\langle {2,0, - 2} \right\rangle \cr
& {\text{ }}{\bf{z}} = \left\langle {5 - 6 - 2,10 - 6 - 0,15 + 3 + 2} \right\rangle \cr
& {\text{ }}{\bf{z}} = \left\langle { - 3,4,20} \right\rangle \cr} $$
