3 and 4 .Determinants and Matrices
medium

$\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$

B

$4 + 7i$

C

$3 + 7i$

D

$7 + 4i$

Solution

(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 $\begin{array}{l}{R_1} \to {R_1} – {R_2}\\{R_2} \to {R_2} – {R_3}\end{array}$

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

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

Standard 12
Mathematics

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