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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
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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