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  • I have a doubt, kindly clarify. - Matrices and Determinants - JEE Main

If 1,\omega ,\omega ^{2} are the cube roots of unity, then

  • Option 1)

    1

  • Option 2)

    \omega

  • Option 3)

    \omega ^{2}

  • Option 4)

    0

 

Answers (2)

best_answer

As we learnt in 

Value of determinants of order 3 -

-

 

 \Delta =\begin{vmatrix} 1 &\omega^{^{n}} &\omega^{2n} \\ \omega^{n} &\omega^{2n} &1 \\ \omega^{2n}&1 &\omega^{n} \end{vmatrix}

C_1 \rightarrow C_1+C_2+C_3

\Delta =\begin{vmatrix} 1+\omega^{^{n}} +\omega^{^{2n}} &\omega^{^{n}} &\omega^{2n} \\ 1+\omega^{^{n}} +\omega^{^{2n}} &\omega^{2n} &1 \\ 1+\omega^{^{n}} +\omega^{^{2n}}&1 &\omega^{n} \end{vmatrix}

for  n\epsilon N , 1+\omega^{^{n}} +\omega^{^{2n}}=0


Option 1)

1

Incorrect option

Option 2)

\omega

Incorrect option

Option 3)

\omega ^{2}

Incorrect option

Option 4)

0

Correct option

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Plabita

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