Answer
$$\mathbf{z}=<7,0,-4>$$
Work Step by Step
$\mathbf{u}=<1,2,3>$, $\mathbf{v}=<2,2,-1>$, and $\mathbf{w}=<4,0,-4>$
Therefore,
$\mathbf{z}=\mathbf{u}-\mathbf{v}+2\mathbf{w}$
$=<1-2+2\times4,2-2+2\times0,3--1+2\times-4>$
$=<7,0,-4>$
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