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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Determinants

NDA 2019 · Mathematics · Determinants

If [ array ccc x & -3 i & 1 y & 1 & i 0 & 2 i & -i array ]=6+11 i ,...

If \left[x−3i1y1i02i−i\begin{array}{ccc}x & -3 i & 1 \\ y & 1 & i \\ 0 & 2 i & -i\end{array}$\right]=6+11 i, then what are the values of xx and y respectively?$

Options

  1. A-3,4
  2. B3,4
  3. C3,-4
  4. D-3,-4

Correct answer

A. -3,4

Step-by-step solution

\left[x−3i1y1i02i−i\begin{array}{ccc}x & -3 i & 1 \\ y & 1 & i \\ 0 & 2 i & -i\end{array}\right]=6+11 i⇒x[−i−(2i)(i)]−y[(−3i)(−i)−(2i)(1)]+0=6+11i⇒x(−i+2)−y(−3−2i)=6+11i⇒−xi+2x+3y+2yi=6+11i⇒(2x+3y)+(−x+2y)i=6+11i∴2x+3y=6 and −x+2y=11\begin{aligned} & \Rightarrow \mathrm{x}[-\mathrm{i}-(2 \mathrm{i})(\mathrm{i})]-\mathrm{y}[(-3 \mathrm{i})(-\mathrm{i})-(2 \mathrm{i})(1)]+0=6+11 \mathrm{i} \\ & \Rightarrow \mathrm{x}(-\mathrm{i}+2)-\mathrm{y}(-3-2 \mathrm{i})=6+11 \mathrm{i} \\ & \Rightarrow-\mathrm{xi}+2 \mathrm{x}+3 \mathrm{y}+2 \mathrm{yi}=6+11 \mathrm{i} \\ & \Rightarrow(2 \mathrm{x}+3 \mathrm{y})+(-\mathrm{x}+2 \mathrm{y}) \mathrm{i}=6+11 \mathrm{i} \\ & \therefore 2 \mathrm{x}+3 \mathrm{y}=6 \text{ and }-\mathrm{x}+2 \mathrm{y}=11\end{aligned}solvingtheequationssolving the equations\begin{aligned} & 2 x+3 y=6 \Rightarrow 2 x+12=6 \\ & \Rightarrow 2 x=-6 \Rightarrow x=-3 \\ & \therefore x=-3, y=4\end{aligned}$$
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