Problem from chapter vector spaces

C35??? Find the rank and nullity of the matrix A = [{1,1,2,-1,1} {0,2,1,0,1} {1,2,1,1,2}]

library(pracma)    #using library pracma to use rank and nullpsace function
## Warning: package 'pracma' was built under R version 3.4.3

Using Rank function - Provides an estimate of the number of linearly independent rows or columns of a matrix M Using nullspace - The kernel (aka null space/nullspace) of a matrix M is the set of all vectors x for which Ax=0

A <- matrix(c(1,1,2,-1,1,0,2,1,0,1,1,2,1,1,2),nrow = 5,ncol = 3)
A
##      [,1] [,2] [,3]
## [1,]    1    0    1
## [2,]    1    2    2
## [3,]    2    1    1
## [4,]   -1    0    1
## [5,]    1    1    2
Rank(A)
## [1] 3
nullspace(A)
## NULL
paste0("Rank of matrix is", Rank(A))
## [1] "Rank of matrix is3"
paste0("Nullity of matrix is", nullspace(A))
## [1] "Nullity of matrix is"

Since nullity says null it means nullity is 0.