If | array ccc r & 2 r-1 & 3 r-2 n 2 & n-1 & a 1 2 n(n-1) & (n-1)^ 2 & 1 2 (n-1)(3 n-4)…
Mathematics · JEE Main · NTA Exams — Matrices and Determinants
If \[\left|\begin{array}{ccc}
r & 2 r-1 & 3 r-2 \\
\frac{n}{2} & n-1 & a \\
\frac{1}{2} n(n-1) & (n-1)^{2} & \frac{1}{2}(n-1)(3 n-4)
\end{array}\right|,\] then the value of \(\sum_{\mathrm{r}=1}^{\mathrm{n}-1} \Delta \mathrm{r}:\)
- depends only on a
- depends only on n
- depends both on a and n
- is independent of both a and n.
Answer
(D) is independent of both a and n.
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