From a122d591c7907c7d62241af3329cf9780359730d Mon Sep 17 00:00:00 2001
From: eneri77 <eneri@77global.biz>
Date: Sun, 23 Feb 2025 11:49:31 +0800
Subject: [PATCH] Update cachematrix.R

---
 cachematrix.R | 53 +++++++++++++++++++++++++++++++++++++++++----------
 1 file changed, 43 insertions(+), 10 deletions(-)

diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..3bb02d376a1 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,48 @@
-## Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
-
+# Function to create a special "matrix" object that can cache its inverse
 makeCacheMatrix <- function(x = matrix()) {
-
+  inv <- NULL  # Variable to store the cached inverse
+  
+  # Function to set the matrix
+  set <- function(y) {
+    x <<- y
+    inv <<- NULL  # Reset the cached inverse when the matrix changes
+  }
+  
+  # Function to get the matrix
+  get <- function() x
+  
+  # Function to set the inverse
+  setInverse <- function(inverse) inv <<- inverse
+  
+  # Function to get the cached inverse
+  getInverse <- function() inv
+  
+  # Return a list of functions to interact with the cache
+  list(set = set, get = get,
+       setInverse = setInverse,
+       getInverse = getInverse)
 }
 
-
-## Write a short comment describing this function
-
+# Function to compute the inverse of the matrix, caching the result
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+  inv <- x$getInverse()  # Check if the inverse is already cached
+  
+  # If cached inverse exists, return it
+  if (!is.null(inv)) {
+    message("Getting cached inverse")
+    return(inv)
+  }
+  
+  # Otherwise, compute the inverse
+  mat <- x$get()
+  inv <- solve(mat, ...)  # Compute inverse using solve()
+  
+  x$setInverse(inv)  # Cache the computed inverse
+  inv
 }
+
+# Example Usage
+m <- matrix(c(2, 1, 3, 4), 2, 2)  # Create a 2x2 invertible matrix
+cachedMatrix <- makeCacheMatrix(m)  # Create a cache matrix object
+cacheSolve(cachedMatrix)  # Compute and cache the inverse
+cacheSolve(cachedMatrix)  # Retrieve the cached inverse