### Assignment: Caching the Inverse of a Matrix

## Description: Matrix inversion is usually a costly computation

## and there may be some benefit to caching the inverse of a

## matrix rather than computing it repeatedly. This pair of

## functions cache the inverse of a matrix.

## This function creates a special "matrix" object

## that can cache its inverse.

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

m <- NULL

# when setting up an object, we set the object and a NULL cached version

set <- function(y) {

x <<- y

m <<- NULL

}

get <- function() x # get function returns the matrix object

# set the inverse of the matrix if "setinverse" is called

setinverse <- function(solve) m <<- solve

# check for a solved version and then solve for an inverse

getinverse <- function() m

list(set = set, get = get,

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

## `cacheSolve` should retrieve the inverse from the cache.

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

# first check to see if there is an inverse already cached

m <- x$getinverse()

if(!is.null(m)) {

message("getting cached data")

return(m)

}

# if the inverse has not been cached, first load the matrix object:

data <- x$get()

# then use the solve function based on the data object just created

m <- solve(data, ...)

# now set a cached version of the inverse

x$setinverse(m)

#and finally, return the resut:

m

}