Chapter 6.3, Problem 29E

In an economics text¹¹ we find the following system:
$\left[\begin{array}{ccc}-R_1& R_1& -\left(1-\alpha \right)\\ \alpha & 1-\alpha & -{\left(1-\alpha \right)}^2\\ R_2& -R_2& \frac{-{\left(1-\alpha \right)}^2}{\alpha }\end{array}\right]\left[\begin{array}{l}d{x}_1\\ d{y}_1\\ dp\end{array}\right]=\left[\begin{array}{l}0\\ 0\\ -R_{2}d{e}_2\end{array}\right].$
Solve for $d{x}_1,d{y}_1$ , and dp. In your answer, you mayrefer to the determinant of the coefficient matrix as D.(You need not compute D.) The quantities $R_1$ , $R_2$ , and D are positive, and $\alpha$ is between zero and one. If $d{e}_2$ is positive, what can you say about the signs of $d{y}_1$ and dp?