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Question: If \(\left| \begin{aligned} & 6i - 3i1 \\ & 43i - 1 \\ & 203i \end{aligned} \right| = x + iy\), t...

If ∣6i−3i143i−1203i∣=x+iy\left| \begin{aligned} & 6i - 3i1 \\ & 43i - 1 \\ & 203i \end{aligned} \right| = x + iy, then

A

x = 3, y=1

B

x =1, y=3

C

x = 0, y=3

D

x = 0, y=0

Answer

x = 0, y=0

Explanation

Solution

Sol. ∣6i−3i143i−1203i∣\left| \begin{aligned} & 6i - 3i1 \\ & 43i - 1 \\ & 203i \end{aligned} \right| Applying C2 →C2+3iC3\rightarrow C_{2} + 3iC_{3}

∣6i0140−1200i∣\left| \begin{aligned} & 6i01 \\ & 40 - 1 \\ & 200i \end{aligned} \right| = 0 = 0+ 0 i,

Equating real and imaginary parts x = 0, y = 0