Answer
$12$
Work Step by Step
In order to work out with the given problem, we will apply some of the following properties of a determinant:
1. The sign of a determinant gets changed when any two columns or two rows are interchanged.
2. When any column or row of a determinant is multiplied by a non-zero number $a$, then the value of the determinant is also multiplied by a non-zero number $a$.
3. When any column or row of a determinant is multiplied by a non-zero number $a$, and then we add it to another column or row, then the value of the determinant does not change.
$D=\begin{vmatrix}{x}&{y}&{z}\\{u}&{v}&{w}\\{1}&{2}&{3}\end{vmatrix}=4$
Multiply $R_3$ by $-3$, and then interchange $R_2$ and $R_3$ to obtain:
$D_{1}=\left|\begin{array}{rrr}{x}&{y}&{z}\\{-3}&{-6}&{-9}\\{u}&{v}&{w}\end{array}\right|$
By property-1 and 2, we have:
$D_{1}=-(-3)D=(3)(4)=12$
