Let $\lbrack x brack$ represent the greatest integer less than or equal to $x$, then the value of the determinant $\left| \begin{matrix} \lbrack e brack & \lbrack\pi brack & \lbrack\pi^{2} - 6 brack \ \lbrack\pi brack & \lbrack\pi^{2} - 6 brack & \lbrack e brack \ \lbrack\pi^{2} - 6 brack & \lbrack e brack & \lbrack\pi brack \end{matrix} ight|$ is

Question

Let $\lbrack xbrack$ represent the greatest integer less than or equal to $x$, then the value of the determinant $\left| \begin{matrix} \lbrack ebrack & \lbrack\pibrack & \lbrack\pi^{2} - 6brack \ \lbrack\pibrack & \lbrack\pi^{2} - 6brack & \lbrack ebrack \ \lbrack\pi^{2} - 6brack & \lbrack ebrack & \lbrack\pibrack \end{matrix} ight|$ is

Dr. Abubacker · Accepted Answer

(a)
$\left| \begin{matrix}
\lbrack ebrack & \lbrack\pibrack & \lbrack\pi^{2} - 6brack \
\lbrack\pibrack & \lbrack\pi^{2} - 6brack & \lbrack ebrack \
\lbrack\pi^{2} - 6brack & \lbrack ebrack & \lbrack\pibrack
\end{matrix} ight|$
$= \left| \begin{matrix}
2 & 3 & 3 \
3 & 3 & 2 \
3 & 2 & 3
\end{matrix} ight|$
$= 2(9 - 4) - 3(9 - 6) + 3(6 - 9)$
$= 10 - 9 - 9$
$= - 8$

Explanation

Reviewed by Dr. Abubacker

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