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DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS1 Mark
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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