Update cachematrix.R

cachematrix.R

@@ -3,13 +3,54 @@
 
 ## Write a short comment describing this function
 
+# makeCacheMatrix creates a special "matrix" object that can cache its inverse
 makeCacheMatrix <- function(x = matrix()) {
-
+    inv <- NULL  # Initialize the cached inverse as NULL
+
+    # Set the matrix value and reset the cached inverse to NULL
+    set <- function(y) {
+        x <<- y      # Store the matrix in the parent environment
+        inv <<- NULL  # Reset cached inverse to NULL whenever the matrix changes
+    }
+
+    # Get the matrix value
+    get <- function() {
+        x
+    }
+
+    # Set the cached inverse of the matrix
+    setInverse <- function(inverse) {
+        inv <<- inverse
+    }
+
+    # Get the cached inverse of the matrix
+    getInverse <- function() {
+        inv
+    }
+
+    # Return a list of functions that can be used to interact with the cache
+    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 the matrix has not changed), 
+# then cacheSolve retrieves the inverse from the cache.
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+    inv <- x$getInverse()  # Try to get the cached inverse
+
+    # If the inverse is already cached, return it with a message
+    if (!is.null(inv)) {
+        message("getting cached data")
+        return(inv)
+    }
+
+    # Otherwise, calculate the inverse of the matrix
+    mat <- x$get()  # Get the matrix
+    inv <- solve(mat, ...)  # Compute the inverse using the solve function
+
+    # Cache the computed inverse
+    x$setInverse(inv)
+
+    return(inv)
 }
+