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1. Evaluate the following determinant:(vii)

    \[\left| \begin{matrix} 1 & 3 & 9 & 27 \\ 3 & 9 & 27 & 1 \\ 9 & 27 & 1 & 3 \\ 27 & 1 & 3 & 9 \\ \end{matrix} \right|\]

contexto.140
  • It is given in the question that,

\left| \begin{matrix} 1 & 3 & 9 & 27 \\ 3 & 9 & 27 & 1 \\ 9 & 27 & 1 & 3 \\ 27 & 1 & 3 & 9 \\ \end{matrix} \right|

Let

Applying , we get

Now applying , we get

Now by applying

Now by applying

So,