Question $2$

Compute the fundamental matrix $N=(I-Q{)}^{-1}$

$N=(I-Q{)}^{-1}=\frac{1}{(0\mathrm{.}6)(0\mathrm{.}9)-(-0\mathrm{.}2)(-0\mathrm{.}1)}\left[\begin{array}{ccc}0\mathrm{.}9& 0\mathrm{.}2& 0\mathrm{.}6\end{array}\right]$

$0\mathrm{.}1=\frac{1}{0\mathrm{.}52}\left[\begin{array}{ccc}0\mathrm{.}9& 0\mathrm{.}2& 0\mathrm{.}6\end{array}\right]$

$0\mathrm{.}1=\left[\begin{array}{ccc}\frac{90}{52}& \frac{20}{52}& \frac{60}{50}\end{array}\right]$

$\frac{10}{52}=\left[\begin{array}{ccc}1\mathrm{.}7308& 0\mathrm{.}3846& 1\mathrm{.}1538\end{array}\right]$

$0\mathrm{.}1923$

$=(I-Q{)}^{-1}=\frac{1}{(0\mathrm{.}6)(0\mathrm{.}9)-(-0\mathrm{.}2)(-0\mathrm{.}1)}\left[\begin{array}{ccc}0\mathrm{.}9& 0\mathrm{.}1& 0\mathrm{.}6\end{array}\right]$

$0\mathrm{.}2=\frac{1}{0\mathrm{.}52}\left[\begin{array}{ccc}0\mathrm{.}9& 0\mathrm{.}1& 0\mathrm{.}6\end{array}\right]$

$0\mathrm{.}2=\left[\begin{array}{ccc}\frac{90}{52}& \frac{10}{52}& \frac{60}{50}\end{array}\right]$

$\frac{20}{52}=\left[\begin{array}{ccc}1\mathrm{.}7308& 0\mathrm{.}1923& 1\mathrm{.}1538\end{array}\right]$

$0\mathrm{.}3846$

$N=(I-Q{)}^{-1}=\frac{1}{(1\mathrm{.}0)(0\mathrm{.}8)-(-0\mathrm{.}1)(-0\mathrm{.}4)}\left[\begin{array}{ccc}0\mathrm{.}8& 0\mathrm{.}4& 1\mathrm{.}0\end{array}\right]$

$0\mathrm{.}1=\frac{1}{0\mathrm{.}76}\left[\begin{array}{ccc}0\mathrm{.}8& 0\mathrm{.}4& 1\mathrm{.}0\end{array}\right]$

$0\mathrm{.}1=\left[\begin{array}{ccc}\frac{40}{38}& \frac{20}{38}& \frac{50}{38}\end{array}\right]$

$\frac{5}{38}=\left[\begin{array}{ccc}1\mathrm{.}0526& 0\mathrm{.}5263& 1\mathrm{.}3158\end{array}\right]$

$0\mathrm{.}1316$

$N=(I-Q{)}^{-1}=\frac{1}{(0\mathrm{.}5)(0\mathrm{.}9)-(-0\mathrm{.}6)(0\mathrm{.}0)}\left[\begin{array}{ccc}0\mathrm{.}9& 0\mathrm{.}0& 0\mathrm{.}5\end{array}\right]$

$0\mathrm{.}6=\frac{1}{0\mathrm{.}45}\left[\begin{array}{ccc}0\mathrm{.}9& 0\mathrm{.}0& 0\mathrm{.}5\end{array}\right]$

$0\mathrm{.}6=\left[\begin{array}{ccc}\frac{90}{45}& 0& \frac{50}{45}\end{array}\right]$

$\frac{60}{45}=\left[\begin{array}{ccc}2\mathrm{.}0000& 0\mathrm{.}0000& 1\mathrm{.}1111\end{array}\right]$

$1\mathrm{.}3333$

None of the above