Find the rank of the matrix \( A \) by reducing its normal form : \( A=\left[\begin{array}{rrrr}1 & 1 & -1 & 1 \\ 1 & -1 & 2 & 1 \\ 3 & 1 & 0 & 1\end{array}\right] \)

Cocoa farming in Ghana is supported by specific agricultural practices. What method is most commonly used for drying cocoa beans after fermentation? a. Sun drying combined with artificial heating b. Employing large-scale solar drying panels c. Using mechanized dryers for rapid drying d. Spreading beans in the open air for six days

A developing nation introduces measures to increase economic productivity per capita. Which theory does this align with? a. Optimum population theory b. Malthusian theory c. Population bomb theory d. Demographic transition model

Corruption has been a persistent issue in West Africa's governance. What is one reason public officials engage in corruption? a. Widespread support for autocratic governance models b. International organizations encourage the privatization of public services c. Strict enforcement of anti-corruption laws by civil society d. Low salaries, poverty, and greed create incentives for bribery

(ix) The equation \( \frac{1}{r r} \frac{\partial}{r}\left(r \frac{\partial u}{r r}\right)=\frac{1}{c^{2}} \frac{\partial^{2} u}{\partial t^{2}} \) is one dimensional wave equation in: (a) Cylindrical coordinate (b) Polar coordinate (c) Spherical coordinate (d) None of these

Export restrictions on cereals like maize anc rice are sometimes imposed in West Africa. What is one primary reason for these restrictions? a. To discourage small-scale farming bavor of industrial agriculture To promote regional trade agreements like ELTS