3 and 4 .Determinants and Matrices
medium

$\Delta = \left| {\,\begin{array}{*{20}{c}}a&{a + b}&{a + b + c}\\{3a}&{4a + 3b}&{5a + 4b + 3c}\\{6a}&{9a + 6b}&{11a + 9b + 6c}\end{array}\,} \right|$ કે જ્યાં $a = i,b = \omega ,c = {\omega ^2}$, તો $\Delta $ મેળવો.

A

$i$

B

$ - {\omega ^2}$

C

$\omega $

D

$ - i$

Solution

(a) We first operating ${R_3} – 2{R_2}$ and ${R_2} – 3{R_1}$ in given determinant, then we get

$ = a[{a^2} + ab – 2{a^2} – ab] = – {a^3} = i$.

Standard 12
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.