Download App

3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
Let $\omega = - \frac{1}{2} + i\frac{{\sqrt 3 }}{2}$. Then the value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{ - 1 - {\omega ^2}}&{{\omega ^2}}\\1&{{\omega ^2}}&{{\omega ^4}}\end{array}\,} \right|$ is
  • A
    $3\omega $
  • ✓
    $3\omega (\omega - 1)$
  • C
    $3{\omega ^2}$
  • D
    $3\omega (1 - \omega )$
✓

Answer

Correct option: B.
$3\omega (\omega - 1)$
b
(b) $\Delta = \left| {\,\begin{array}{*{20}{c}}3&1&1\\0&{ - 1 - {\omega ^2}}&{{\omega ^2}}\\0&{{\omega ^2}}&\omega \end{array}\,} \right|$

$({C_1} \to {C_1} + {C_2} + {C_3})$

$(\because\,\,1 + \omega  + {\omega ^2} = 0)$

$ = 3\,[\omega .\omega - {\omega ^4}] = 3({\omega ^2} - \omega )$ $ = 3\omega (\omega - 1)$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 3 and 4 . determinant and metrices→3 and 4 . determinant and metrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\int\frac{1}{(\text{x}+2)(\text{x}^2+1)}\text{ dx}=\text{a}\log|1+\text{x}^2|+\text{b}\tan^{-1}\text{x}+\frac{1}{5}\log|\text{x}+2|+\text{C},$ then
  1. $\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
  2. $\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
  3. $\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
  4. $\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
→
Mark the correct alternative in the following question:
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If $\frac{\text{P(X = r})}{\text{P(X = n} -\text{r})}$ is independent of n and r, then p equals:
  1. $\frac{1}{2}$
  2. $\frac{1}{3}$
  3. $\frac{1}{5}$
  4. $\frac{1}{7}$
→
Let X be a discrete random variable. Then the variance of X is:
→
If $x = \sin t$ and $y = \sin pt$, then the value of $\left( {1 - {x^2}} \right){{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} + {p^2}y$ is equal to
→
The lateral edge of a regular hexagonal pyramid is $1 cm$. If the volume is maximum, then its height must be equal to
→
If $a,b,c$ are unequal what is the condition that the value of the following determinant is zero $\Delta = \left| {\,\begin{array}{*{20}{c}}a&{{a^2}}&{{a^3} + 1}\\b&{{b^2}}&{{b^3} + 1}\\c&{{c^2}}&{{c^3} + 1}\end{array}\,} \right|$
→
Let $r_k=\frac{\int_0^1\left(1-x^7\right)^k d x}{\int_0^1\left(1-x^7\right)^{k+1} d x}, k \in N$. Then the value of $\sum_{\mathrm{k}=1}^{10} \frac{1}{7\left(\mathrm{r}_{\mathrm{k}}-1\right)}$ is equal to ...........
→
If $\varphi (x) = \int_{1/x}^{\sqrt x } {\sin ({t^2})\,dt,} $ then $\phi '(1) = $
→
If $\text{x}=\text{a}\cos^3\theta,\text{y}=\text{a}\sin^3,$ then $\sqrt{1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2}=$
  1. $\tan^2\theta$
  2. $\sec^2\theta$
  3. $\sec^2\theta$
  4. $|\sec\theta|$
→
Let $f (x) =\int\limits_1^x {\left( {t\,\ln (t) - \frac{{\ln \,t}}{t}} \right)\,dt} (x > 1) $ then
→