diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..69893d1b6ff 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,51 @@
-## Put comments here that give an overall description of what your
-## functions do
+## Programming Assignment 2: Lexical Scoping
+##
+## In this assignment we use the <<- operator which can be used to assign 
+## a value to an object in an environment that is different from the current 
+## environment. makeCacheMatrix and cacheSolve are two functions that 
+## create a special object that stores a numeric matrix 
+## and cache's its inverse.
 
-## Write a short comment describing this function
-
-makeCacheMatrix <- function(x = matrix()) {
+## makeCacheMatrix: creates a special "matrix" object 
+## that can cache its inverse.
 
+makeCacheMatrix <- function(m = matrix()) {
+  m_inv <- NULL
+  set <- function(y) {
+    m <<- y
+    m_inv <<- NULL   # Clear the inverse when the matrix changes.
+  }
+  get <- function() m
+  setinverse <- function(y) m_inv<<- y
+  getinverse <- function() m_inv
+  list(set = set, 
+       get = get,
+       setinverse = setinverse,
+       getinverse = getinverse)
 }
 
+## cacheSolve: computes the inverse of the special "matrix" 
+## returned by makeCacheMatrix. If the inverse has already 
+## been calculated (and the matrix has not changed), then 
+## return the cached inverse. Otherwise solve for the inverse, 
+## cache the solution, and return the result.
+##
+## For this assignment we assume that the matrix supplied is
+## always invertible.
 
-## Write a short comment describing this function
-
-cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+cacheSolve <- function(m, ...) {
+  ## Return a matrix that is the inverse of m
+  m_i <- m$getinverse()
+  
+  ## If m_i is not null we have a cached solution.
+  if(!is.null(m_i)) {
+    message("Using cached result.")
+    return(m_i)
+  }
+  
+  # Otherwise m_i is null and needs to be solved.
+  data <- m$get()
+  m_i <- solve(data, ...)    
+  m$setinverse(m_i)
+  m_i
 }