Answer
$<4, 3, -3>$
$$
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Work Step by Step
The question asks for the vectors $ u + v$, $u - v$, and $3u - 0.5 v$
Given $u = <0, 1, -3>$ and $v = <4, 2, 0>$
$u + v = <0 + 4, 1 + 2, -3 + 0)> = <4, 3, -3>$
$u - v = <0 - 4, 1 - 2, -3 - 0)> = $
$3u - 0.5v = 3<0, 1, -3> - 0.5 <4, 2, 0>$
$= <0 - 2, 3 - 1, -9 - 0> = $