## Put comments here that give an overall description of what your

## functions do

## These two functions cache the inverse of a matrix, to avoid computing

## the inverse of a unchanged matrix repeatedly

## Write a short comment describing this function

## This function creates a "matrix" object, which can cache its inverse.

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

x_inv <- NULL

set <- function(y){

x<<-y

x_inv<<-NULL

}

get <- function()x

setinverse <- function(inverse)x_inv<<- inverse

getinverse <- function()x_inv

list(set = set, get = get,

setinverse = setinverse,

getinverse = getinverse)

}

## Write a short comment describing this function

## This function computes the inverse of the "matrix" object created by

## the function makeCacheMatrix above. This function should retrieve

## the inverse from the cache, if the inverse was calculated

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

## Return a matrix that is the inverse of 'x'

x_inv <- x$getinverse()

if(!is.null(x_inv)) {

message("getting cached data")

return(x_inv)

}

data <- x$get()

x_inv <- solve(data, ...)

x$setinverse(x_inv)

x_inv

}