\( \operatorname{det}\left[\begin{array}{cc}\sum_{k=0}^{n} k & \sum_{k=0}^{n}{ }^{n} C_{k} k...

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\( \operatorname{det}\left[\begin{array}{cc}\sum_{k=0}^{n} k & \sum_{k=0}^{n}{ }^{n} C_{k} k^{2} \\ \sum_{k=0}^{n}{ }^{n} C_{k} k & \sum_{k=0}^{n}{ }^{n} C_{k} 3^{k}\end{array}\right]=0 \)
holds for some positive integer \( n \). Then math xmlns=http://www.w3.org/1998/Math/MathMLmunderovermo∑/momrowmik/mimo=/momn0/mn/mrowmn4/mn/munderovermfracmmultiscriptsmic/mimik/minone/mprescripts/none/min/mi/mmultiscriptsmrowmik/mimo+/momn1/mn/mrow/mfrac/math=
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