6. The goods market and money market of an economy are described by the following
equations
C = 0.8 Yd
I = 100 – 2r
G = 150
X = 50
Md = 0.5Y – 5r
Ms = 250
where C is consumption, Yd is disposable income, I is investment, r is the rate
of interest, G is government expenditure, X is export, Md is demand for money,
and Ms is supply of money. This economy does not import anything, has no
transfer payments by the government, and its government taxes are fixed at 200.
Assuming there is simultaneous equilibrium in both markets, use both the inverse
matrix method and Cramer’s rule to solve for equilibrium level of income and the
equilibrium rate of interest in this economy.

No idea how to covert this into a matrix.




Also

(20) 2. A company earns before-tax profits of $100,000. It has agreed to contribute 10
percent of its after-tax profits to the Red Cross Relief Fund. It must pay a provincial
tax of 5 percent of its profits (after the Red Cross donation) and a federal tax of 40
percent of its profit (after the donation and provincial taxes are paid). Use Cramer’s
rule to determine how much the company pays in provincial taxes, federal taxes, and
Red Cross donation. {Hint: Let C, P, and F represent the amounts of the charitable
donation, provincial tax, and federal tax, respectively. Since after-tax profits are
$100,000 – (P+F), therefore: C = 0.1 [100,000 – (P+F) ]. Use the other pieces of
for F. Now solve these equations simultaneously using Cramer’s rule.}

This one i figured
C=0.1[100,000-(P+F)]
P=0.05[100.000-C]
F=0.4[100,000-(P-C)]

But once again no idea how to convert to matrix and proceed

For the first one, I don't know how to convert that jumble to a matrix either, but once you figure out how to set up the equations you can do the same that I did in the second problem shown below.

To convert to a matrix, you need to have n equations and n unknowns written in the format:

ax + by + cz = d
ex + fy + gz = h
ix + jy + kz = l

then the matrix becomes
[a b c] [d]
|e f g| = |h|
[i j k] [l]

So for 3 equations 3 unknowns, you would have a 3x3 matrix and a 1x3 matrix.

Find the determinant of the 3x3 matrix.

For Cramer's rule, you substitute the 1x3 into each column and solve the matrix.

Here's the work. I'm assuming you know how to solve for determinants.

I should note that it is vitally important that you get the equations set up correctly and the matrices set up correctly. After that it is just plug and chug, but if you make any mistakes in the matrix/equations you will get a very wrong answer.



This post was edited by Dontrunaway on Nov 4 2014 11:42pm

Thank you I had actaully already found this but you answers helped to know i was doing it right!