If 6i & -3i & 1 4 & 3i & -1 20 & 3 & i =x… - Vidyadip

MCQ

If $ \begin{vmatrix} 6\text{i} &\text{amp;} -3\text{i} &\text{amp;} 1\\ 4 &\text{amp; } 3\text{i} &\text{amp;} -1 \\ 20 &\text{amp; } 3 &\text{amp; i}\end{vmatrix}=\text{x}+\text{iy},$ then?

A
$x = 3, y = 1$
B
$x = 1, y = 3$
C
$x = 0, y = 3$
✓
$x = 0, y = 0$

✓

Answer

Correct option: D.

$x = 0, y = 0$

$ \begin{vmatrix} 6\text{i} &\text{amp;} -3\text{i} &\text{amp;} 1\\ 4 &\text{amp; } 3\text{i} &\text{amp;} -1 \\ 20 &\text{amp; } 3 &\text{amp; i}\end{vmatrix}=\text{x}+\text{iy},$
$\Rightarrow6\text{i}(3\text{i}^2+3)+3\text{i}(4\text{i}+20)+1(12-60\text{i})=\text{x}+\text{iy}$
$\Rightarrow0=\text{x}+\text{iy}$
$\therefore \text{x}=\text{y}=0$

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