Exercises: C40, page 215 Solve a system of equations using the inverse of a matrix.

library(matlib)

A <- matrix(data = c(1, 1, 3, 1, -2, -1, -4, -1, 
                     1, 4, 10, 2, 0, -2, -4, 5),
            nrow = 4, ncol = 4, byrow = T)
b <- matrix(data = c(5, -7, 9, 9), byrow = F, nrow = 4, ncol = 1)

print(A)
##      [,1] [,2] [,3] [,4]
## [1,]    1    1    3    1
## [2,]   -2   -1   -4   -1
## [3,]    1    4   10    2
## [4,]    0   -2   -4    5
print(b)
##      [,1]
## [1,]    5
## [2,]   -7
## [3,]    9
## [4,]    9
Ai <- inv(A)

X <- Ai %*% b
print(X)
##            [,1]
## [1,]  2.7142857
## [2,]  2.2857143
## [3,] -0.7142857
## [4,]  2.1428571