For problems C10–C19, find all solutions to the system of linear equations. Use your favorite computing device to row-reduce the augmented matrices for the systems, and write the solutions as a set, using correct set notation.

Problem C10

Traditional Method Matrix

A=matrix(c(2,-3,1,7,2,8,-4,5,1,3,-3,0,-5,2,3,4),nrow=4,byrow=TRUE)
b=matrix(c(14,-1,4,-19), nrow=4)
#solve(A,b)


print(A) 
##      [,1] [,2] [,3] [,4]
## [1,]    2   -3    1    7
## [2,]    2    8   -4    5
## [3,]    1    3   -3    0
## [4,]   -5    2    3    4

Using Solve

solve(A,b)
##      [,1]
## [1,]    1
## [2,]   -3
## [3,]   -4
## [4,]    1

PRACMA

require(pracma)
augA=matrix(c(2, -3, 1, 7, 14,2,8,-4,5,-1, 1,3,-3,0,4, -5, 2, 3, 4,-19),nrow=4,byrow=TRUE)
augA
##      [,1] [,2] [,3] [,4] [,5]
## [1,]    2   -3    1    7   14
## [2,]    2    8   -4    5   -1
## [3,]    1    3   -3    0    4
## [4,]   -5    2    3    4  -19
rref(augA)
##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    0    0    0    1
## [2,]    0    1    0    0   -3
## [3,]    0    0    1    0   -4
## [4,]    0    0    0    1    1

\[ S =\begin{pmatrix} 1 \\ -3 \\ -4 \\ 1\\ \end{pmatrix}\]