Question $6(6$ marks$)$

Given a $2-$by$-2$ multiple$-$input multiple$-$output system:

The signals received at the receiver $(Rx)$ are:

$y_1(t)=([-0\mathrm{.}648,-0\mathrm{.}365,0\mathrm{.}260,-0\mathrm{.}041,-0\mathrm{.}435])$

$y_2(t)=([-0\mathrm{.}105,0\mathrm{.}282,0\mathrm{.}395,-0\mathrm{.}024,0\mathrm{.}202])$

It is given that the channel coefficients are $(a,b,c,d)=(0\mathrm{.}25,-0\mathrm{.}62,0\mathrm{.}38,-0\mathrm{.}17).$ Estimate the transmission signals $x_1(t)$ and $x_2(t).$ Show all your calculation steps clearly.

Hint: Use the mathematical fact on matrix inverse:

$G=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]G^{-1}=\frac{1}{ad-bc}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right],if,ad-bc0$