cachematrix.R

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

  m <- NULL 
       set <- function(y) { 
                    x <<- y ## assign the input matrix y to the variable x in the 
                   ## parent environment 
                    m <<- NULL ## re-initialize m in the parent environment to null 
             } 
           get <- function() x ## return the matrix x 
           setinverse <- function(inverse) m <<- inverse ## set the cache m equal 
          ## to the inverse of the matrix x 
         getinverse <- function() m ## return the cached inverse of x 
          list(set = set, get = get, 
                            setinverse = setinverse, 
                            getinverse = getinverse) 
  } 



cacheSolve <- function(x, ...) { 
          ## Return a matrix that is the inverse of 'x' 
           
         m <- x$getinverse() 
         if(!is.null(m)) { 
                   message("getting cached data") 
                   return(m) 
           } 
        data <- x$get() 
         m <- solve(data, ...) 
          x$setinverse(m) 
          m 
 }