The problem is to find the determinant of a given matrix: $$ A = \begin{pmatrix} 7 & 4 & 0 & ... & 0 \\ 3 & 7 & 4 & ... & 0 \\ 0 & 3 & 7 & ... & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & ... & 7 \end{pmatrix}. $$ I am able to express the determinant in recurrence relation $ a_{n}=7a_{n-1} - 12a_{n-2} $. Solving this, I get the formula: $ a_{n} = 4\cdot 4^{n} - 3\cdot3^{n} ,\, n\geq 1$. It's good, but I'm more intrested in row/column play. I tried to add everything to the first column, so I get a bunch of 14's, I can make them turn to 1, but it does nothing. Maybe I'm missing something.
2026-04-24 06:31:48.1777012308
Determinant of nxn almost diagonal matrix
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