The value of the determinant 1 beginvmatrix 10 - - 11 - - 12 - - 111- - -2- - 13- -I12- - 13- - 14-Wend vmatrix is

The correct option is D 2(10 ! 11 ! 12 !)10! amp;11! amp;12! 11! amp;12! amp;13! 12! amp; 13! amp; 14! = 10! 11! 12! 1 amp;11 ...

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Evaluation of a Determinant

The value of ...

Question

The value of the determinant $∣ ∣ ∣ ∣ \begin{matrix} 10! & 11! & 12! 11! & 12! & 13! 12! & 13! & 14! \end{matrix} ∣ ∣ ∣ ∣$ is

2(10! 11!)

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2(10 ! 13 !)

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2(10 ! 11 ! 12 !)

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2(11 ! 12 ! 13 !)

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∣ ∣ ∣ ∣ \begin{matrix} 10! & 11! & 12! 11! & 12! & 13! 12! & 13! & 14! \end{matrix} ∣ ∣ ∣ ∣ =

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Evaluate the determinants..

$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 4 & 5 1 & 1 & - 2 2 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 0 & 1 & 2 - 1 & 0 & - 3 - 2 & 3 & 0 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & - 2 0 & 2 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

∣ ∣ ∣ ∣ \begin{matrix} 10! & 11! & 12! 11! & 12! & 13! 12! & 13! & 14! \end{matrix} ∣ ∣ ∣ ∣

\frac{1}{4 - \sqrt{15}} - \frac{1}{\sqrt{15} - \sqrt{14}} + \frac{1}{\sqrt{14} - \sqrt{13}} - \frac{1}{\sqrt{13} - \sqrt{12}} + \frac{1}{\sqrt{12} - \sqrt{11}} - \frac{1}{\sqrt{11} - \sqrt{10}} + \frac{1}{\sqrt{10} - 3}

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