DATA 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS

C17 p42

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.

\(−x_1 + 5x_2 = −8\)

\(−2x_1 + 5x_2 + 5x_3 + 2x_4 = 9\)

\(−3x_1 − x_2 + 3x_3 + x_4 = 3\)

\(7x_1 + 6x_2 + 5x_3 + x_4 = 30\)

d <- c(-1, 5, 0, 0, -2, 5, 5, 2, -3, -1, 3, 1, 7, 6, 5, 1)
(A <- matrix(d, ncol = 4, byrow = T))

##      [,1] [,2] [,3] [,4]
## [1,]   -1    5    0    0
## [2,]   -2    5    5    2
## [3,]   -3   -1    3    1
## [4,]    7    6    5    1

(b <- c(-8, 9, 3, 30))

## [1] -8  9  3 30

solve(A, b)

## [1]  3 -1  2  5