From dbb6885c82a169de8362f46cf7d262f7bdc22c6d Mon Sep 17 00:00:00 2001
From: baoanh1809-byte <baoanh1809@gmail.com>
Date: Tue, 23 Jun 2026 21:14:17 +0700
Subject: [PATCH 1/3] Add files via upload

---
 cachematrix.R | 57 +++++++++++++++++++++++++++++++++++++--------------
 1 file changed, 42 insertions(+), 15 deletions(-)

diff --git a/cachematrix.R b/cachematrix.R
index a50be65aa44..9b656caf3ad 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,15 +1,42 @@
-## Put comments here that give an overall description of what your
-## functions do
-
-## Write a short comment describing this function
-
-makeCacheMatrix <- function(x = matrix()) {
-
-}
-
-
-## Write a short comment describing this function
-
-cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
-}
+makeCacheMatrix <- function(x = matrix()) {
+  inv <- NULL
+  
+  set <- function(y) {
+    x <<- y
+    inv <<- NULL
+  }
+  
+  get <- function() x
+  
+  setinverse <- function(inverse) {
+    inv <<- inverse
+  }
+  
+  getinverse <- function() {
+    inv
+  }
+  
+  list(
+    set = set,
+    get = get,
+    setinverse = setinverse,
+    getinverse = getinverse
+  )
+}
+
+
+cacheSolve <- function(x, ...) {
+  inv <- x$getinverse()
+  
+  if(!is.null(inv)) {
+    message("getting cached data")
+    return(inv)
+  }
+  
+  data <- x$get()
+  inv <- solve(data, ...)
+  
+  x$setinverse(inv)
+  
+  inv
+}

From 654745cb1a360c33a64826bb0b599e5980672a5b Mon Sep 17 00:00:00 2001
From: baoanh1809-byte <baoanh1809@gmail.com>
Date: Tue, 23 Jun 2026 21:20:00 +0700
Subject: [PATCH 2/3] Add files via upload


From 0e3fd2825a38682687f88f5f3ad2619e083aa3e1 Mon Sep 17 00:00:00 2001
From: baoanh1809-byte <baoanh1809@gmail.com>
Date: Fri, 26 Jun 2026 18:51:18 +0700
Subject: [PATCH 3/3] cachematrix.R

---
 cachematrix.R | 29 +++++++++++++++++++----------
 1 file changed, 19 insertions(+), 10 deletions(-)

diff --git a/cachematrix.R b/cachematrix.R
index 9b656caf3ad..a33ecdf382c 100644
--- a/cachematrix.R
+++ b/cachematrix.R
@@ -1,21 +1,28 @@
+## These functions cache the inverse of a matrix so that the inverse
+## is computed only once. If the inverse has already been calculated,
+## the cached value is returned instead of recomputing it.
+
+## Create a special matrix object that can store a matrix and cache
+## its inverse.
+
 makeCacheMatrix <- function(x = matrix()) {
   inv <- NULL
-  
+
   set <- function(y) {
     x <<- y
     inv <<- NULL
   }
-  
+
   get <- function() x
-  
+
   setinverse <- function(inverse) {
     inv <<- inverse
   }
-  
+
   getinverse <- function() {
     inv
   }
-  
+
   list(
     set = set,
     get = get,
@@ -24,19 +31,21 @@ makeCacheMatrix <- function(x = matrix()) {
   )
 }
 
+## Return the cached inverse if available; otherwise compute the
+## inverse, cache it, and return it.
 
 cacheSolve <- function(x, ...) {
   inv <- x$getinverse()
-  
-  if(!is.null(inv)) {
+
+  if (!is.null(inv)) {
     message("getting cached data")
     return(inv)
   }
-  
+
   data <- x$get()
   inv <- solve(data, ...)
-  
+
   x$setinverse(inv)
-  
+
   inv
 }