If a,b,c and d are complex numbers, then the determinant = | , * … - Vidyadip

MCQ

If $a,b,c$ and $d $ are complex numbers, then the determinant $\Delta = \left| {\,\begin{array}{*{20}{c}}2&{a + b + c + d}&{ab + cd}\\{a + b + c + d}&{2(a + b)(c + d)}&{ab(c + d) + cd(a + b)}\\{ab + cd}&{ab(c + d) + cd(a + d)}&{2abcd}\end{array}} \right|$is

A
Dependent on $a, b, c$ and $ d$
✓
Independent of $a,b,c$and $d$
C
Dependent on $a,c$and independent of $b,d$
D
None of these

✓

Answer

Correct option: B.

Independent of $a,b,c$and $d$

b
(b) We can write the given determinant as a product of two determinants as follows $\Delta = 0\,.\,0 = 0$ (on simplification), which is independent of $a, b, c $ and $d.$

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