Matrix inverses

mi.R

set.seed(23)
# Create a positive-definite matrix 
# a Wishart random variable + the identity matrix should fullfil this. Any positive-definite matrix is invertible.
m <- rWishart(.1, 5, diag(5))[,,1] + diag(5)

# set the bottom and right to 1
# by this the top left is positive definite, but the complete matrix is singular, i.e. not invertible
m[4:5, ] <- 1
m[, 4:5] <- 1

# works
solve(m[1:3, 1:3])
# fails, due to rank deficiency
solve(m)[1:3, 1:3]