Update cachematrix.R with complete functions

cachematrix.R

@@ -1,15 +1,53 @@
-## Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
+## These functions create a special matrix object that can cache its inverse
+## and compute the inverse using caching for efficiency.
 
+## makeCacheMatrix: Creates a special "matrix" object that can cache its inverse
 makeCacheMatrix <- function(x = matrix()) {
-
+    # Initialize the inverse as NULL
+    inv <- NULL
+
+    # Set the matrix
+    set <- function(y) {
+        x <<- y
+        inv <<- NULL  # Reset inverse when matrix changes
+    }
+
+    # Get the matrix
+    get <- function() x
+
+    # Set the inverse
+    setinverse <- function(inverse) inv <<- inverse
+
+    # Get the inverse
+    getinverse <- function() inv
+
+    # Return a list of functions
+    list(set = set,
+         get = get,
+         setinverse = setinverse,
+         getinverse = getinverse)
 }
 
-
-## Write a short comment describing this function
-
+## cacheSolve: Computes the inverse of the special "matrix" returned by makeCacheMatrix
+## If the inverse has already been calculated (and matrix hasn't changed), 
+## then retrieves inverse from cache
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+    # Get cached inverse
+    inv <- x$getinverse()
+
+    # If inverse exists in cache, return it
+    if(!is.null(inv)) {
+        message("getting cached data")
+        return(inv)
+    }
+
+    # Otherwise, compute the inverse
+    data <- x$get()
+    inv <- solve(data, ...)
+
+    # Cache the inverse
+    x$setinverse(inv)
+
+    # Return the inverse
+    inv
 }