1. [9 Marks] Briefly define the following concepts:
a) Domain of a function
b) Singular matrix
c) equilibrium
2. [8 Marks] Given the matrix
$\begin{pmatrix} 1 & 3 & 3 & 1 \ 0 & 0 & 3 & 2 \ 1 & 3 & 2 & 1 \ -1 & 4 & 1 & 2 \end{pmatrix}$ find
a) The minor $M_{43}$
b) The cofactor $C_{43}$
3. [20 Marks] Given the sets $S_1 = \{9, 8, 2\}$, $S_2 = \{one, two, three\}$, $S_3 = \{3, 6, 9, 8, 7\}$, $S_4 = \{1, 2$
a) Find
i) $S_1 \cup S_4$
ii) $S_1 \cap S_4$
iii) Subsets of $S_2$
iv) $S_1 \times S_3$ Cartesian plan
b) Is $S_2 = S_4$? Explain your answer.
c) State and demonstrate the distributive law using $S_1$, $S_3$ and $S_4$.
4. [10 Marks] Find the partial market equilibrium for the following goods market model:
$Q_d = 4 - p^2$
$Q_s = 4P - 1$
5. [8 Marks] Given the following Keynesian national income model:
$Y = C + I_0 + G_0$
$C = 25 + 6Y^{1/2}$
a) Identify the endogenous and exogenous variables of the model.
b) If $I_0 = 16$ and $G_0 = 14$, find $Y^*$ and $C^*.$
