# Example of a generalized inverse
X <- rbind(1:3, 2*(1:3), c(1,0,1))
# solve(X)  # Error
MASS::ginv(X)
X
X %*% MASS::ginv(X) %*% X

# Conditional independence and precision matrix
n <- 100000
x <- rnorm(n)
y <- x + rnorm(n)
z <- y + rnorm(n)
cor(cbind(x, y, z))
cor(cbind(x, y, z)) |> solve()