Question

If $\left|\begin{array}{ccc}3i& -9i& 1\\ 2& 9i& -1\\ 10& 9& i\end{array}\right|=x+iy$, then

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

Answer 1

Answer: (D)

We have,
$\left|\begin{array}{ccc}3i& -9i& 1\\ 2& 9i& -1\\ 10& 9& i\end{array}\right|=x+iy$
$\Rightarrow \left|\begin{array}{ccc}3i+2& 0& 0\\ 2& 9i& -1\\ 10& 9& i\end{array}\right|=x+iy$
$\left[\because R_1\to R_1+R_2\right]$
$\Rightarrow (3i+2)\left[9i^2+9\right]=x+iy$
$\Rightarrow (3i+2)(-9+9)=x+iy\left[\because i^2=-1\right]$
$\Rightarrow 0=x+iy$
$\Rightarrow x=0,y=0$