defined the functions makeCacheMatrix and cacheSolve

cachematrix.R

@@ -1,15 +1,37 @@
 ## Put comments here that give an overall description of what your
 ## functions do
 
-## Write a short comment describing this function
+## this function returns a list of functions.
+## the functions within the list all have their scope set within the parent function
+## the functions within the list allow us to cache a matrix, retrieve a cached matrix, 
+## cache inverse of the cached matrix, retrieve cached inverse of the a cached matrix
 
 makeCacheMatrix <- function(x = matrix()) {
-
+  i <- NULL
+  set <- function(y) {
+    x <<- y
+    i <<- NULL
+  }
+  get <- function() x
+  setinverse <- function() {
+    i <<- solve(x)
+  }
+  getinverse <- function() i
+  list(set=set,get=get,setinverse=setinverse,getinverse=getinverse)
 }
 
 
-## Write a short comment describing this function
+## this function returns the inverse of the cached matrix within the variable
+## the functions first checks if the inverse is cached and sends the cached results back if condition is true
+## if the inverse of the matrix isn't cached the the function solves for the inverse, caches it, and shares back the result
 
 cacheSolve <- function(x, ...) {
         ## Return a matrix that is the inverse of 'x'
+  i <- x$getinverse()
+  if (!is.null(i)){
+    message("from the cache")
+    return(i)
+  }
+  i <- x$setinverse()
+  i
 }