Symbolic matrices
Task number: 2601
Calculate determinants of the following symbolic matrices:
Variant 1
\( \begin{pmatrix} a_1+x & a_2 & a_3 & … & a_n \\ a_1 & a_2+x & a_3 & … & a_n \\ a_1 & a_2 & a_3+x & … & a_n \\ \vdots & \vdots &\vdots & \ddots & \vdots \\ a_1 & a_2 & a_3 & … & a_n+x \\ \end{pmatrix} \)
Variant 2
\( \begin{pmatrix} x & -1 & 0 & … & 0 \\ 0 & x & -1 & \ddots & \vdots \\ \vdots & \ddots &\ddots & \ddots & 0 \\ 0 & … & 0 & x & -1 \\ a_0 & a_1 & … & a_{n-1} & a_n \\ \end{pmatrix} \)
Variant 3
\( \begin{pmatrix} a+1 & a & 0 & … & 0 \\ 1 & a+1 & a & \ddots & \vdots \\ 0 & 1 & a+1 & \ddots & 0 \\ \vdots & \ddots &\ddots & \ddots & a \\ 0 & … & 0 & 1 & a+1 \\ \end{pmatrix} \)