# These functions owe a lot to the example given in the programming assignment.

# The comments in some cases are tedious, but required for novices.

## This function creates a special "matrix" object that can cache its inverse.

makeCacheMatrix <- function(x = matrix()) {

m <- NULL # m should exist in this context.

set <- function(y) { # a function to set matrix and clear inverse.

x <<- y # assign x and m in their parent contexts.

m <<- NULL

}

get <- function() x # get, a simple function to get the matrix.

setinverse <- function(inverse) m <<- inverse # assign inverse in its parent context.

getinverse <- function() m # getinverse, a simple function to get the inverse.

list(set = set, get = get, # our list of functions

setinverse = setinverse,

getinverse = getinverse)

}

## This function computes the inverse of the special "matrix"

## returned by makeCacheMatrix above. If the inverse has already

## been calculated (and the matrix has not changed), then the

## cacheSolve should retrieve the inverse from the cache.

cacheSolve <- function(x, ...) {

## Return a matrix that is the inverse of 'x'

m <- x$getinverse()

if(!is.null(m)) { # It wasn't null, so its known!

message("getting cached data")

return(m)

}

data <- x$get() # Bring the data into this context

m <- solve(data) # The function that calculates the inverse is solve.

x$setinverse(m) # set the inverse (in a couple contexts up)

m # return the inverse

}