Chapter 4.6, Problem 1ED

Refer to the mathematical model in Example 4:

$\begin{array}{c}A\\ \left[\begin{array}{cc}1& 1\\ 0.05& 0.1\end{array}\right]\end{array}\begin{array}{c}X\\ \left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]\end{array}=\left[\begin{array}{c}B\\ \begin{array}{l}{k}_1\\ k_2\end{array}\end{array}\right]$

(A) Does matrix equation (3) always have a solution for any constant matrix $B$ ?

(B) Do all these solutions make sense for the original problem? If not, give examples.

(C) If the total investment is $k_1=\text{\$10,000}$, describe all possible annual returns $k_2$.