Suppose that the following system of equations describe the economy of a hypotheticalcountry:( ) ( )Y C Y I i G= + +: IS or goods market( , )M L i YP =: LM or money marketa) Get the total differentials of the above system of equations and put them inmatrix representation

To get the total differentials of the system of equations, we first need to differentiate each equation with respect to its variables.

For the IS or goods market equation: Y = C(Y) + I(i) + G

The total differential is: dY = C'(Y)dY + I'(i)di + dG

For the LM or money market equation: M = L(i, Y)P

The total differential is: dM = L_Y dY + L_i di + P dL

Now, we can put these differentials into a matrix representation. The matrix would look like this:

| dY | = | C'(Y) , I'(i) | | dY | | | | , | | | | dM | = | L_Y , L_i + P | | dL |

Where C'(Y) is the derivative of C with respect to Y, I'(i) is the derivative of I with respect to i, L_Y is the partial derivative of L with respect to Y, and L_i is the partial derivative of L with respect to i.