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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
$\left| {\,\begin{array}{*{20}{c}}{1 + i}&{1 - i}&i\\{1 - i}&i&{1 + i}\\i&{1 + i}&{1 - i}\end{array}\,} \right| = $
  • A
    $ - 4 - 7i$
  • ✓
    $4 + 7i$
  • C
    $3 + 7i$
  • D
    $7 + 4i$
✓

Answer

Correct option: B.
$4 + 7i$
b
(b) $\Delta = (2 + i)\,\left| {\,\begin{array}{*{20}{c}}1&1&i\\1&{1 + 2i}&{1 + i}\\1&2&{1 - i}\end{array}\,} \right|\,$

=$(2 + i)$$\left| {\,\begin{array}{*{20}{c}}0&{ - 2i}&{ - 1}\\0&{ - 1 + 2i}&{2i}\\1&2&{1 - i}\end{array}\,} \right|$          by $\begin{array}{l}{R_1} \to {R_1} - {R_2}\\{R_2} \to {R_2} - {R_3}\end{array}$

= $(2 + i)\,\,\{ - 4{i^2} + ( - 1 + 2i)\} = (2 + i)\,(4 - 1 + 2i)$

= $(2 + i)\,(3 + 2i) = 4 + 7i$.

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