Matrix od order n
Task number: 2599
Calculate the determinant of the following real matrix
\( \begin{pmatrix} 1 & 2 & 3 & 4 & 5 & … & n \\ -1 & 0 & 2 & 3 & 4 & … & n-1 \\ -1 & -2 & 0 & 3 & 4 & … & n-1 \\ -1 & -2 & -3 & 0 & 4 & … & n-1 \\ -1 & -2 & -3 & -4 & 0 & … & n-1 \\ \vdots & \vdots & \vdots & \vdots & & \ddots & \\ -1 & -2 & -3 & -4 & … & 1-n & 0 \\ \end{pmatrix} \).
Resolution
We add the first row to all remaining ones.
Result
The determinant of the matrix is \(n!\).
