605D1

Find all Solutions to this linear system:

x + y - z = -5 x - y - z = -3 x + y + z = 0

M <- matrix(c(1,1,-1,-5,1,-1,-1,-3,1,1,1,0),nrow = 3, byrow = TRUE)

M

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

M[3,] <- M[2,]+ M[3,]

M

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

M[2,] <- M[2,]-M[1,]

M

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

X <- M[3,4]/M[3,1]

X

## [1] -1.5

Y <- M[2,4]/M[2,2]
Y

## [1] -1

Z <- (M[1,4]-M[1,2]*Y - M[1,1]*X)/M[1,3]
Z

## [1] 2.5