Complex Numbers 1 Question 7
7. If $\left|\begin{array}{ccc}6 i & -3 i & 1 \ 4 & 3 i & -1 \ 20 & 3 & i\end{array}\right|=x+i y$, then
(1998, 2M)
(a) $x=3, y=1$ (b) $x=1, y=1$ (c) $x=0, y=3$
(d) $x=0, y=0$
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Answer:
Correct Answer: 7. (d)
Solution:
- Given, $\begin{array}{crrl}6 i & -3 i & 1 \ 4 & 3 i & -1 \ 20 & 3 & i\end{array}=x+i y$
$$ \Rightarrow \quad \begin{array}{rrrrl} & 6 i & 1 & 1 & \\ & -3 i & 4 & -1 & -1 \end{array}=x+i y $$
$$ \Rightarrow \quad x+i y=0\left[\because C _2 \text { and } C _3 \text { are identical }\right] $$
$$ \Rightarrow \quad x=0, y=0 $$
