D.C37

Find the rank and nullity of the Matrix A

\[ A = \left[ {\begin{array}{cc} 3 & 2 & 1 & 1 & 1\\ 2 & 3 & 0 & 1 & 1\\ -1 & 1 & 2 & 1 & 0\\ 1 & 1 & 0 & 1 & 1\\ 0 & 1 & 1 & 2 & -1\\ \end{array} } \right] \]

using the Matrix and pracma package to solve this question:

library(Matrix)
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:pracma':
## 
##     expm, lu, tril, triu
library(pracma)

A <-matrix(c(3,2,-1,1,0,2,3,1,1,1,1,0,2,0,1,1,1,1,1,2,1,1,0,1,-1), nrow=5,ncol=5)

A
##      [,1] [,2] [,3] [,4] [,5]
## [1,]    3    2    1    1    1
## [2,]    2    3    0    1    1
## [3,]   -1    1    2    1    0
## [4,]    1    1    0    1    1
## [5,]    0    1    1    2   -1
rankMatrix(A)
## [1] 5
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 1.110223e-15
nullspace(A)
## NULL

We get that the rank is 5 and the nullity is 0