If be a complex cube root of unity, then | , * 20 c 1& & - ^2 /2 … - Vidyadip

MCQ

If $\omega $ be a complex cube root of unity, then $\left| {\,\begin{array}{*{20}{c}}1&\omega &{ - {\omega ^2}/2}\\1&1&1\\1&{ - 1}&0\end{array}\,} \right| = $

✓
$0$
B
$1$
C
$\omega $
D
${\omega ^2}$

✓

Answer

Correct option: A.

$0$

a
(a) $\left| {\,\begin{array}{*{20}{c}}1&\omega &{ - {\omega ^2}/2}\\1&1&1\\1&{ - 1}&0\end{array}\,} \right| = - \frac{1}{2}\left| {\,\begin{array}{*{20}{c}}1&\omega &{{\omega ^2}}\\1&1&{ - 2}\\1&{ - 1}&0\end{array}\,} \right|$

= $ - \frac{1}{2}\left| {\,\begin{array}{*{20}{c}}0&\omega &{{\omega ^2}}\\0&1&{ - 2}\\0&{ - 1}&0\end{array}\,} \right| = 0$, (Apply ${C_1} \to {C_1} + {C_2} + {C_3})$.

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 STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int\limits^1_0\frac{\text{d}}{\text{dx}}\Big\{\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)\Big\}\text{dx}$ is equal to:

The magnitude of the vector $6 \hat{i}-2 \hat{j}+3 \hat{k}$ is

If $A$ and $B$ are two matrices of order $3\times m$ and $3\times n$ respectively and $m = n,$ then the order of $5A - 2B$ is:

A bag contains 5 red and 3 blue balls are drawn at random without replacement, then the probability of getting exactly one red ball is.

If the function f : R → A given by $\text{f(x)}=\frac{\text{x}^2}{\text{x}^2+1}$ is a surjection, then A =

$\lim\limits_{\text{n}\rightarrow\infty}\Big\{\frac{1}{2\text{n}+1}+\frac{1}{2\text{n}+2}+\ .....+\frac{1}{2\text{n}+\text{n}}\Big\}$ is equal to:

Let $\mathrm{f}:(-1, \infty) \rightarrow \mathrm{R}$ be defined by $\mathrm{f}(0)=1$ and $f(x)=\frac{1}{x} \log _{e}(1+x), x \neq 0 .$ Then the function $f$

If one ball is drawn ar random from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, then the probability that 2 white and 1 black balls will be drawn is.

If ${e^y} + xy = e$, then the value of ${{{d^2}y} \over {d{x^2}}}$ for $x = 0$, is

If $f\left( x \right) = {\sin ^{ - 1}}\left( {\frac{{2 \times {3^x}}}{{1 + {9^x}}}} \right)$, then $f'(-\frac {1}{2})$ equals