Answer
$12$
Work Step by Step
We use one or a combination of theorems (11) to (15).
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Starting with
$D=\left|\begin{array}{lll}{x}&{y}&{z}\\{u}&{v}&{w}\\{1}&{2}&{3}\end{array}\right|$,
multiplying row 3 with $-3$,
and then interchanging rows 2 and 3, we obtain
$D_{1}=\left|\begin{array}{rrr}{x}&{y}&{z}\\{-3}&{-6}&{-9}\\{u}&{v}&{w}\end{array}\right|$
By theorem (11),
The value of a determinant changes sign if any two rows (or any two columns) are interchanged,
and by theorem (14),
If any row (or any column) of a determinant is multiplied by a nonzero number $k,$ the value of the determinant is also changed by a factor of $k$,
it follows that
$D_{1}=-(-3)D=+3(4)=12$
