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  4. If Δ=|6 i -3 i w 4 3 i -w 20 3 i w|=x+i y, then

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Q. If $\Delta=\begin{vmatrix}6 i & -3 i & w \\ 4 & 3 i & -w \\ 20 & 3 & i w\end{vmatrix}=x+i y$, then

Determinants

Solution:

We can write
$\Delta=-3 i w\begin{vmatrix} 6 i & 1 & 1 \\ 4 & -1 & -1 \\ 20 & i & i \end{vmatrix}=0 $
$\therefore x=0, y=0$