cachematrix.R

## 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 assignment is a pair of functions that cache the inverse of a matrix.

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


## a sample invertable matrix is made with cbind(c(2,4,5), c(3,6,7), c(9,3,1))

makeCacheMatrix <- function(x = matrix()) {
  m <- NULL
  set <- function(y) {
    x <<- y
    m <<- NULL
  }
  get <- function() x
  setsolve <- function(solve) m <<- solve
  getsolve <- function() m
  list(set = set, get = get,
       setsolve = setsolve,
       getsolve = getsolve)
}


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