Find the inverse of the coefficients matrix what

Question

1. Given the condition of market equilibrium, the demand function, and the supply function as follows

Q_d = Q_s
Q_d= 220 - 5P
Q_s= -20 + 3P

a) Rewrite this set of equations into a matrix format.

b) Find the inverse of the coefficients matrix.

c) Use the Inverse method to find the values of all three variables at the equilibrium.

d) Use the Cramer's rule to find the values of all three variables at the equilibrium. Are they equal to what you found in c) ?

2. Let the national income model be:

Y = C + I_o + G
C=a + b (Y - To) (a > 0, 0 < b < 1)
G = gY (0 < g

Y is the National Income. C is Consumption. G is Government Expenditure. T_o is Net Taxes. I_o is Investment. Investment and Net Taxes are exogenous variables. (as a guide you can look at Schaum's p. 247)

a) Rewrite this set of equations into a matrix format

b) Find the inverse of the coefficients matrix

c) What restriction on the parameters is needed for a solution to exist? In other words, what restriction is needed in order to make the coefficients matrix non-singular?

d) Use the Inverse method to find the equilibrium values of National Income(Y), Consumption (C) , and Government Expenditure (G).

e) Use the Cramer's rule to find the values of all three variables at the equilibrium. Are they equal to what you found in d)?