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

A=matrix(c(2, -3, 1, 7,2,8,-4,5, 0,1,3,-3, -5, 2, 3, 4),nrow=4,byrow=TRUE)
b=matrix(c(14,-1,4,-19), nrow=4)
solve(A)%*%(b)
##            [,1]
## [1,]  4.7213303
## [2,] -0.5653670
## [3,]  1.6892202
## [4,]  0.1674312

PRACMA

require(pracma)
augA=matrix(c(2, -3, 1, 7, 14,2,8,-4,5,-1, 0,1,3,-3,4, -5, 2, 3, 4,-19),nrow=4,byrow=TRUE)
rref(augA)
##      [,1] [,2] [,3] [,4]       [,5]
## [1,]    1    0    0    0  4.7213303
## [2,]    0    1    0    0 -0.5653670
## [3,]    0    0    1    0  1.6892202
## [4,]    0    0    0    1  0.1674312

\[ S =\begin{pmatrix} 4.721 \\ -0.565 \\ 1.689 \\ 0.167\\ \end{pmatrix}\]