#Linear Algebra using R

set.seed(302010)

#Set the dimensions
n<-10
p<-3

#Generate the values for the X matrix
#As an example, use rnorm to generate Normal variates.
xvals<-rnorm(n*p)

(X<-matrix(xvals,nrow=n,ncol=p))

#Set the n values for y

y<-rnorm(n)

##########################################

#Matrix multiplication

b<-c(3,-2,1)

#Result of Xb multiplication
(X%*%b)

#System Xb = y is over-determined.

XtX<-t(X) %*% X

Xty<-t(X) %*% y

#Solve the now exactly determined system
b<-solve(XtX,Xty)

#Now use solve in a slightly different way
#Compute the inverse first
XtXinv<-solve(XtX)

(b<-XtXinv %*% Xty)