KShaffer_Discussion1

For Discussion 1, I’ve selected problem C33 from the SLE Chapter of “A First Course in Linear Algebra”.

The problem is as follows:

Find all solutions to the linear system:
\[x + y - z = -1\] \[x - y - z = -1\] \[z = 2\]

A <- matrix(c(1,1,-1,1,-1,-1,0,0,1), nrow = 3, ncol = 3)
A

##      [,1] [,2] [,3]
## [1,]    1    1    0
## [2,]    1   -1    0
## [3,]   -1   -1    1

b <- matrix(c(-1,-1,2), nrow = 3, ncol = 1)
b

##      [,1]
## [1,]   -1
## [2,]   -1
## [3,]    2

(A.b <- cbind(A,b))

##      [,1] [,2] [,3] [,4]
## [1,]    1    1    0   -1
## [2,]    1   -1    0   -1
## [3,]   -1   -1    1    2

solve(A,b)

##      [,1]
## [1,]   -1
## [2,]    0
## [3,]    1

Therefore, our answers are: \[x = -1\] \[y = 0\] \[z = 1\]