#==================================================================
# R script to: (a) Solve a system of k equations in k unknowns,
# represented by the matrix equation Ax = c, where A is a k X k
# matrix c is a k X 1 column vector of constants, and x is a k X 1
# column vector of unknown values. (b) Calculate the inverse of the
# matrix A, if an inverse exists.
#==================================================================

#------------------------------------------------------------------
#  Enter rows of matrix A and elements of vector c here.
#------------------------------------------------------------------
A=rbind(c(-1,4),c(3,6))
c=c(8,30)

#------------------------------------------------------------------
#  (a)  Solve system of linear equations.
#------------------------------------------------------------------
x=solve(A,c)

#------------------------------------------------------------------
#  (b)  Invert matrix A.
#------------------------------------------------------------------
Ainv=solve(A)

#------------------------------------------------------------------
#  Print results to the console.
#------------------------------------------------------------------
Ainv
Ainv%*%A