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it's a ex. what i need to do exactly how this is written in pdf and i don't know how to do in this same lane this two big matrixes

i need to do this ex and i have no idea how to posit this two big matrix's how can i sole it this is my latex code. Sorry of my bbcode but i'm rly bad in such a thinks, and my english is not very good as you can see.

$$ f(x) =
\left \{
\begin{array} {rl}
sin (\frac {1}{x}) & \mbox {dla} \ x \neq 0 ...

I'm very thankfull for that but i have another question how to get Theata on middle of this table maybe u have any idea?? Ok nevermind i solve the problem but i need to do something like that:

what is problem with that
$$ D=(\left[ \begin{array} {ccc |ccc}
a_1,_1 & \ldots & a_1,_n & & & \\
\vdots & \ddots & \vdots & & \Theta &\\
a_n,_1 & \ldots & a_n,_n & & & \\
\hline
& & & & b_1,_1 & \ldots & b_1,_n \\
& &\Theta & & \vdots & \ddots & \vdots \\
& & & & b_n,_1 & \ldots & b_n,_n ...