Inverting Matrix

In order to save some computational time, there are important theoretical properties of matrix operations. We begin with some properties of matrix operations in this section

library(matlib)
A <- matrix(c(1,-2,-1,2,3,2,3,-2,1), nrow = 3, ncol = 3)
inv(A)

##             [,1]       [,2]       [,3]
## [1,]  0.58333333  0.3333333 -1.0833333
## [2,]  0.33333333  0.3333333 -0.3333333
## [3,] -0.08333333 -0.3333333  0.5833333

Then, R returns

library(MASS)
fractions(inv(A))

##      [,1]   [,2]   [,3]  
## [1,]   7/12    1/3 -13/12
## [2,]    1/3    1/3   -1/3
## [3,]  -1/12   -1/3   7/12

we can use the solve() function to find the inverse of a matrix instead of the inv() function.

library(matlib)
A <- matrix(c(1,-2,-1,2,3,2,3,-2,1), nrow = 3, ncol = 3)
solve(A)

##             [,1]       [,2]       [,3]
## [1,]  0.58333333  0.3333333 -1.0833333
## [2,]  0.33333333  0.3333333 -0.3333333
## [3,] -0.08333333 -0.3333333  0.5833333