left| {,begin{array}{*{20}{c}}{1 + i}&{1 | vedclass

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Question

(b) $\Delta = (2 + i)\,\left| {\,\begin{array}{*{20}{c}}1&1&i\1&{1 + 2i}&{1 + i}\1&2&{1 - i}\end{array}\,} ight|\,$

=$(

Vedclass · Accepted Answer

$4 + 7i$

Vedclass · Answer

(b) $\Delta = (2 + i)\,\left| {\,\begin{array}{*{20}{c}}1&1&i\1&{1 + 2i}&{1 + i}\1&2&{1 - i}\end{array}\,} ight|\,$

=$(2 + i)$$\left| {\,\begin{array}{*{20}{c}}0&{ - 2i}&{ - 1}\0&{ - 1 + 2i}&{2i}\1&2&{1 - i}\end{array}\,} ight|$          by $\begin{array}{l}{R_1} 	o {R_1} - {R_2}\{R_2} 	o {R_2} - {R_3}\end{array}$

= $(2 + i)\,\,\{ - 4{i^2} + ( - 1 + 2i)\} = (2 + i)\,(4 - 1 + 2i)$

= $(2 + i)\,(3 + 2i) = 4 + 7i$.

$\left| {\,\begin{array}{*{20}{c}}{1 + i}&{1 - i}&i\\{1 - i}&i&{1 + i}\\i&{1 + i}&{1 - i}\end{array}\,} \right| = $

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