The model of the national income balance is known as follows: Y = C + I₀ + G₀ (1) C = a + b ( - T) ( > 0.0 < b < 1) (2) T = tY (0 < < 1) (3) Y= national income;

C= household consumption;

I₀= investment;

G₀= governmen expenditure

T= tax

t= tax rate.

The first equation is a condition for the occurrence of a balance of national income in a country economy without trade with other economies. Meanwhile, the second equation and third is function. a. If, from the above model, the value of national income, household consumption, ladder, and taxes at equilibrium (or when the first equation is satisfied), determine the endogenous variables, exogenous variables, and the parameters of the system of equations, then arrange the equation matrix! b. Use the Laplace expansion in the first row to determine the determinant and the condition non-singularity coefficient matrix! Does the system of equations have a unique solution? Explain! c. Use the matrix theorem to get the value of national income, household consumption ladder, and tax revenues are in balance if the following values are known:

I₀ =7,500,

G₀, = 2,500,

a = 2,000

b = 2/3,

t= 25%