#
# Need to install: 
# 
# sudo apt-get install r-cran-rgl
#
# to get the following to work.
#
if( !require('matlib') ){
   install.packages('matlib', dependencies=TRUE, repos='http://cran.rstudio.com/')
}
library(matlib)

# Problem 10:
#
A = matrix(c(1, 4, -2, 3), nrow=2, ncol=2, byrow=TRUE)
print(echelon(cbind(A, diag(2)))) #, verbose=TRUE, fractions=TRUE)

# Problem 11:
#
A = matrix(c(3, -1, 6, 2), nrow=2, ncol=2, byrow=TRUE)
print(echelon(cbind(A, diag(2)), fractions=TRUE))

# Problem 12:
#
A = matrix(c(1, 2, 3, 2, 4, 5, 3, 5, 6), nrow=3, ncol=3, byrow=TRUE)
print(echelon(cbind(A, diag(3)))) #, verbose=TRUE, fractions=TRUE)

# Problem 13:
#
A = matrix(c(1, 1, -1, 2, -1, 1, 1, 1, 2), nrow=3, ncol=3, byrow=TRUE)
print(echelon(cbind(A, diag(3)))) #, verbose=TRUE, fractions=TRUE)

# Problem 14:
#
A = matrix(c(1, 2, 1, -2, 1, 8, 1, -2, -7), nrow=3, ncol=3, byrow=TRUE)
print(echelon(cbind(A, diag(3)))) #, verbose=TRUE, fractions=TRUE)

# Problem 15:
#
A = matrix(c(2, 1, 0, 0, 2, 1, 0, 0, 2), nrow=3, ncol=3, byrow=TRUE)
print(echelon(cbind(A, diag(3)))) #, verbose=TRUE, fractions=TRUE)

# Problem 16:
#
A = matrix(c(1, -1, -1, 2, 1, 0, 3, -2, 1), nrow=3, ncol=3, byrow=TRUE)
print(echelon(cbind(A, diag(3)))) #, verbose=TRUE, fractions=TRUE)

# Problem 17:
#
A = matrix(c(2, 3, 1, -1, 2, 1, 4, -1, -1), nrow=3, ncol=3, byrow=TRUE)
print(echelon(cbind(A, diag(3)))) #, verbose=TRUE, fractions=TRUE)

# Problem 18:
#
A = matrix(c(1, 0, 0, -1, 0, -1, 1, 0, -1, 0, 1, 0, 0, 1, -1, 1), nrow=4, ncol=4, byrow=TRUE)
print(echelon(cbind(A, diag(4)))) #, verbose=TRUE, fractions=TRUE)

# Problem 19:
#
A = matrix(c(1, -1, 2, 0, -1, 2, -4, 2, 1, 0, 1, 3, -2, 2, 0, -1), nrow=4, ncol=4, byrow=TRUE)
print(echelon(cbind(A, diag(4)))) #, verbose=TRUE, fractions=TRUE)