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While trying to simplify a solution I came up with the following sparse matrix but don't know how to solve it. [tex] [A(t)][X] = 0 [/tex]

[tex]

$\left(

\begin{array}{ccccc}

A_0(t) & 1 & 1 & ... & 1 \\

A_1(t) & 1 & 0 & ... & 0 \\

... & ... & ... & ... & ... \\

A_{n-1}(t) & 0 & ... & 1 & 0 \\

A_n(t) & 0 & ... & 0 & 1 \\

\end{array}

\right)

\left(

\begin{array}{c}

x_0 \\

x_1 \\

... \\

x_{n-1} \\

x_n

\end{array}

\right)

= 0

$

[/tex]

I need to find solutions for [tex]t[/tex] satisfying [tex]|A(t)| = 0[/tex]

I would really appreciate if you would point me in finding out

1. Whether there is actually an analytic solution for this

2. If not a suitable numerical technique to find solutions

Thanks

Krindik

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