Answer
$4$
Work Step by Step
We use one or a combination of theorems (11) to (15).
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Starting with
$D=\left|\begin{array}{lll}{x}&{y}&{z}\\{u}&{v}&{w}\\{1}&{2}&{3}\end{array}\right|$,
if we add $(-1)\times$(column 1) to column 3, we obtain
$D_{1}= \left|\begin{array}{lll}{x}&{y}&{z-x}\\{u}&{v}&{w-u}\\{1}&{2}&{2}\end{array}\right|.$
$D_{1}=D=4$
