FzahirDiscussionResponse2

Constructing the matrix and calculating determinant

A <- matrix(c(1, 2, 1, 2, 0, 1, 2, 3, 7/4), nrow=3, byrow=T)
A

##      [,1] [,2] [,3]
## [1,]    1    2 1.00
## [2,]    2    0 1.00
## [3,]    2    3 1.75

print(det(A))

## [1] 0

Trying to find inverse using solve

print(solve(A))
##Error: Lapack routine dgesv: system is exactly singular: U[3,3] = 0

Using Ginv from matlib to solve for generalized inverse

library('matlib')
Ainv<-Ginv(A)
Ainv

##      [,1]       [,2]      [,3]
## [1,]    0  0.5000000 0.0000000
## [2,]    0 -0.3333333 0.3333333
## [3,]    0  0.0000000 0.0000000

Test AAinverseA to see if it returns the original matrix

test<-A%*%Ainv%*%A
test

However the generalised Moore-Penrose does not return an identity matrix when I multiply A*Ainverse

identity<-A%*%Ainv
identity

##      [,1]        [,2]      [,3]
## [1,]    0 -0.16666666 0.6666667
## [2,]    0  1.00000000 0.0000000
## [3,]    0  0.00000001 1.0000000