Problem 3 page 41

Using R to build the matrix

a<-matrix(c(2,3,-1,0,1,2,1,3,1,3,3,7), nrow=3, byrow=TRUE)
a
##      [,1] [,2] [,3] [,4]
## [1,]    2    3   -1    0
## [2,]    1    2    1    3
## [3,]    1    3    3    7
b<-matrix(c(0,3,7),nrow=3)
b
##      [,1]
## [1,]    0
## [2,]    3
## [3,]    7

Results:

X1=1, X2=0, X3=2

Row echelon using pracma package

library('pracma')
c<-rref(a)
c
##      [,1] [,2] [,3] [,4]
## [1,]    1    0    0    1
## [2,]    0    1    0    0
## [3,]    0    0    1    2

Solving using matrix commands in R

a1<-matrix(c(2,3,-1,1,2,1,1,3,3), nrow=3, byrow=TRUE)
a1
##      [,1] [,2] [,3]
## [1,]    2    3   -1
## [2,]    1    2    1
## [3,]    1    3    3
b1<-matrix(c(0,3,7), nrow=3)
b1
##      [,1]
## [1,]    0
## [2,]    3
## [3,]    7
c1<-solve(a1)%*%b1
c1
##      [,1]
## [1,]    1
## [2,]    0
## [3,]    2