Question

If $\begin{vmatrix}3i&-9i&1\\\ 2&9i&-1\\\ 10&9&i\end{vmatrix} = x + iy$, then

• A. x = 1, y = 1
• B. x = 0, y = 1
• C. x = 1, y = 0
• D. x = 0, y = 0

Answer 1

Answer: (D)

x = 0, y = 0

Answer 2

We have,
$\begin{vmatrix}3 i & -9 i & 1 \\\ 2 & 9 i & -1 \\\ 10 & 9 & i\end{vmatrix}=x +i y$
$\Rightarrow\begin{vmatrix}3 i+2 & 0 & 0 \\\ 2 & 9 i & -1 \\\ 10 & 9 & i\end{vmatrix}=x +i y$
$\left[\because R_{1} \rightarrow R_{1}+R_{2}\right]$
$\Rightarrow (3 i+2)\left[9 i^{2}+9\right]=x +i y$
$\Rightarrow (3 i+2)(-9+9)=x +i y\, \left[\because i^{2}=-1\right]$
$\Rightarrow 0=x +i y$
$\Rightarrow x=0, y=0$