library(openxlsx)

dat<-read.xlsx("http://kanggc.iptime.org/book/data/macro-simple-e.xlsx")

A<-as.matrix(dat)

H<-matrix(c(0,200,0,100,40,100), nrow=6)
H
X<-t(solve(A)%*%H)
XV<-as.vector(X)
names(XV)<-c("Y=","C=","Yd=","T=","I=","G=")
XV

IH<-matrix(c(0,200,0,100,80,100), nrow=6)
IX<-t(solve(A)%*%IH)
IXV<-as.vector(IX)
names(IXV)<-c("Y=","C=","Yd=","T=","I=","G=")
IXV

IM<-(IXV[1]-X[1,1])/(IXV[5]-H[5,1])
names(IM)<-c("dY/dI=")
IM

GH<-matrix(c(0,200,0,100,40,200), nrow=6)
GX<-t(solve(A)%*%GH)
GXV<-as.vector(GX)
names(GXV)<-c("Y=","C=","Yd=","T=","I=","G=")
GXV

GM<-(GXV[1]-X[1,1])/(GXV[6]-H[6,1])
names(GM)<-c("dY/dG=")
GM