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 \(n!\).

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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