<s>[INST] Determinant of a General Expression Matrix I don't really know how to do this question:
" Let $A = $
$\begin{pmatrix}1 & 1& 1 & \cdots & 1 \\ 1 & 1-x & 1 & \cdots & 1 \\ 1 & 1& 2-x &\cdots & 1 \\ \cdots & \cdots & \cdots & \cdots & \cdots \\ 1& 1 & 1 &\cdots& n-1-x \end{pmatrix}$"
be an n×n matrix with n≥3. Solve the equation det(A)=0 of x∈R and find the largest root. 
 [/INST] Subtract the first column from the last, then $$\det A=\det\begin{pmatrix}1 & 1& 1 & \cdots & 1 & 0 \\ 1 & 1-x & 1 & \cdots & 1 & 0 \\ 1 & 1& 2-x &\cdots & 1 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 1& 1 & 1 &\cdots& n-2-x & 0\\1& 1 & 1 &\cdots& 1 & n-2-x \end{pmatrix}=$$$$(n-2-x)\det\begin{pmatrix}1 & 1& 1 & \cdots & 1 \\ 1 & 1-x & 1 & \cdots & 1 \\ 1 & 1& 2-x &\cdots & 1 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1& 1 & 1 & \cdots& n-2-x \end{pmatrix}.$$ How can you continue from here?
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